refactor: move analysis admin commands into psysonic-analysis (M6/7)

Reframed M6 from "extract psysonic-commands" to "place each domain's
Tauri commands in its own domain crate" — the original psysonic-commands
proposal would have been a thin shell with no clear domain ownership
because each prior milestone already kept its own commands inline:

  audio_*_commands           in psysonic-audio
  cache/sync commands        in psysonic-syncfs
  navidrome/discord/etc      in psysonic-integration

The leftover analysis admin commands (7 of them) logically belong to
the analysis domain. So they move there:

  src/lib_commands/app_api/analysis.rs   →
    crates/psysonic-analysis/src/commands.rs

  WaveformCachePayload + LoudnessCachePayload  moved out of top-crate
                                               lib.rs into commands.rs

PlaybackQueryHandle gets a second closure (`should_defer_backfill`) so
analysis_enqueue_seed_from_url can ask "is a ranged playback already
going to seed this track?" without depending on psysonic-audio.

Top crate keeps the shell-flavored commands (window/tray/mini-player,
greet/exit_app, mpris/global-shortcuts/check_dir_accessible, perf,
cli_bridge) for M7 to clean up.

Behaviour preserving. Cargo check + clippy --workspace clean.

src-tauri/crates/psysonic-analysis/src/commands.rs

@@ -0,0 +1,263 @@
+//! Tauri commands that read/write the analysis cache and steer the backfill
+//! queue. Thin wrappers around `analysis_cache::*` and `analysis_runtime::*`
+//! plus the playback-query port (for "is this track currently playing? /
+//! is a ranged playback already going to seed it?").
+
+use std::collections::HashSet;
+
+use tauri::Manager;
+
+use psysonic_core::ports::PlaybackQueryHandle;
+
+use crate::analysis_cache;
+use crate::analysis_runtime::{
+    analysis_backfill_is_current_track, analysis_backfill_shared, prune_analysis_queues,
+    AnalysisBackfillEnqueueKind,
+};
+
+#[derive(serde::Serialize)]
+#[serde(rename_all = "camelCase")]
+pub struct WaveformCachePayload {
+    pub bins: Vec<u8>,
+    pub bin_count: i64,
+    pub is_partial: bool,
+    pub known_until_sec: f64,
+    pub duration_sec: f64,
+    pub updated_at: i64,
+}
+
+#[derive(serde::Serialize)]
+#[serde(rename_all = "camelCase")]
+pub struct LoudnessCachePayload {
+    pub integrated_lufs: f64,
+    pub true_peak: f64,
+    pub recommended_gain_db: f64,
+    pub target_lufs: f64,
+    pub updated_at: i64,
+}
+
+#[tauri::command]
+pub fn analysis_get_waveform(
+    track_id: String,
+    md5_16kb: String,
+    cache: tauri::State<'_, analysis_cache::AnalysisCache>,
+) -> Result<Option<WaveformCachePayload>, String> {
+    let key = analysis_cache::TrackKey {
+        track_id: track_id.clone(),
+        md5_16kb: md5_16kb.clone(),
+    };
+    let row = cache.get_waveform(&key)?;
+    match &row {
+        Some(v) => {
+            crate::app_deprintln!(
+                "[analysis][waveform] db hit (exact key) track_id={} md5_16kb={} bins_len={} bin_count={} updated_at={}",
+                track_id,
+                md5_16kb,
+                v.bins.len(),
+                v.bin_count,
+                v.updated_at
+            );
+        }
+        None => {
+            crate::app_deprintln!(
+                "[analysis][waveform] db miss (exact key) track_id={} md5_16kb={}",
+                track_id,
+                md5_16kb
+            );
+        }
+    }
+    Ok(row.map(|v| WaveformCachePayload {
+        bins: v.bins,
+        bin_count: v.bin_count,
+        is_partial: v.is_partial,
+        known_until_sec: v.known_until_sec,
+        duration_sec: v.duration_sec,
+        updated_at: v.updated_at,
+    }))
+}
+
+#[tauri::command]
+pub fn analysis_get_waveform_for_track(
+    track_id: String,
+    cache: tauri::State<'_, analysis_cache::AnalysisCache>,
+) -> Result<Option<WaveformCachePayload>, String> {
+    let row = cache.get_latest_waveform_for_track(&track_id)?;
+    match &row {
+        Some(v) => {
+            crate::app_deprintln!(
+                "[analysis][waveform] db hit track_id={} bins_len={} bin_count={} updated_at={}",
+                track_id,
+                v.bins.len(),
+                v.bin_count,
+                v.updated_at
+            );
+        }
+        None => {
+            crate::app_deprintln!(
+                "[analysis][waveform] db miss track_id={}",
+                track_id
+            );
+        }
+    }
+    Ok(row.map(|v| WaveformCachePayload {
+        bins: v.bins,
+        bin_count: v.bin_count,
+        is_partial: v.is_partial,
+        known_until_sec: v.known_until_sec,
+        duration_sec: v.duration_sec,
+        updated_at: v.updated_at,
+    }))
+}
+
+#[tauri::command]
+pub fn analysis_get_loudness_for_track(
+    track_id: String,
+    target_lufs: Option<f64>,
+    cache: tauri::State<'_, analysis_cache::AnalysisCache>,
+) -> Result<Option<LoudnessCachePayload>, String> {
+    let row = cache.get_latest_loudness_for_track(&track_id)?;
+    Ok(row.map(|v| {
+        let requested_target = target_lufs.unwrap_or(v.target_lufs).clamp(-30.0, -8.0);
+        let recommended_gain_db = analysis_cache::recommended_gain_for_target(
+            v.integrated_lufs,
+            v.true_peak,
+            requested_target,
+        );
+        LoudnessCachePayload {
+            integrated_lufs: v.integrated_lufs,
+            true_peak: v.true_peak,
+            recommended_gain_db,
+            target_lufs: requested_target,
+            updated_at: v.updated_at,
+        }
+    }))
+}
+
+#[tauri::command]
+pub fn analysis_delete_loudness_for_track(
+    track_id: String,
+    cache: tauri::State<'_, analysis_cache::AnalysisCache>,
+) -> Result<u64, String> {
+    cache.delete_loudness_for_track_id(&track_id)
+}
+
+#[tauri::command]
+pub fn analysis_delete_all_waveforms(
+    cache: tauri::State<'_, analysis_cache::AnalysisCache>,
+) -> Result<u64, String> {
+    cache.delete_all_waveforms()
+}
+
+#[tauri::command]
+pub fn analysis_enqueue_seed_from_url(
+    track_id: String,
+    url: String,
+    force: Option<bool>,
+    app: tauri::AppHandle,
+) -> Result<(), String> {
+    if track_id.trim().is_empty() || url.trim().is_empty() {
+        return Ok(());
+    }
+    let force = force.unwrap_or(false);
+    if !force {
+        if let Some(playback) = app.try_state::<PlaybackQueryHandle>() {
+            if playback.ranged_loudness_backfill_should_defer(&track_id) {
+                crate::app_deprintln!(
+                    "[analysis] backfill skip track_id={} reason=ranged_playback_will_seed",
+                    track_id
+                );
+                return Ok(());
+            }
+        }
+    }
+    if !force {
+        if let Some(cache) = app.try_state::<analysis_cache::AnalysisCache>() {
+            if cache.get_latest_loudness_for_track(&track_id)?.is_some() {
+                crate::app_deprintln!(
+                    "[analysis] backfill skip (already cached): {}",
+                    track_id
+                );
+                return Ok(());
+            }
+        }
+    }
+    let tid_log = track_id.clone();
+    let high_priority = analysis_backfill_is_current_track(&app, &track_id);
+    let shared = analysis_backfill_shared(&app);
+    let kind = {
+        let mut st = shared
+            .state
+            .lock()
+            .map_err(|_| "analysis backfill lock poisoned".to_string())?;
+        st.enqueue(track_id, url, high_priority)
+    };
+    match kind {
+        AnalysisBackfillEnqueueKind::NewBack | AnalysisBackfillEnqueueKind::NewFront => {
+            shared.ping_worker();
+            crate::app_deprintln!(
+                "[analysis] backfill enqueued: track_id={} position={}",
+                tid_log,
+                if high_priority { "front" } else { "back" }
+            );
+        }
+        AnalysisBackfillEnqueueKind::ReorderedFront => {
+            shared.ping_worker();
+            crate::app_deprintln!(
+                "[analysis] backfill bumped to front (current track) track_id={}",
+                tid_log
+            );
+        }
+        AnalysisBackfillEnqueueKind::DuplicateSkipped | AnalysisBackfillEnqueueKind::RunningSkipped => {}
+    }
+    Ok(())
+}
+
+#[derive(Debug, Clone, serde::Serialize)]
+#[serde(rename_all = "camelCase")]
+pub struct AnalysisPrunePendingResult {
+    pub keep_count: usize,
+    pub http_removed: usize,
+    pub cpu_removed_jobs: usize,
+    pub cpu_removed_waiters: usize,
+}
+
+/// Prunes pending analysis work for tracks no longer present in the playback queue.
+///
+/// Keeps currently-running jobs untouched; only queued (not-yet-started) jobs are removed.
+#[tauri::command]
+pub fn analysis_prune_pending_to_track_ids(
+    track_ids: Vec<String>,
+) -> Result<AnalysisPrunePendingResult, String> {
+    let mut normalized: Vec<String> = Vec::with_capacity(track_ids.len());
+    let mut seen = HashSet::new();
+    for raw in track_ids {
+        let tid = raw.trim();
+        if tid.is_empty() {
+            continue;
+        }
+        if seen.insert(tid.to_string()) {
+            normalized.push(tid.to_string());
+        }
+    }
+    let keep_track_ids: HashSet<&str> = normalized.iter().map(|s| s.as_str()).collect();
+
+    let (http_removed, cpu_removed_jobs, cpu_removed_waiters) =
+        prune_analysis_queues(&keep_track_ids)?;
+
+    if http_removed > 0 || cpu_removed_jobs > 0 {
+        crate::app_deprintln!(
+            "[analysis] pruned pending queues keep={} removed_http={} removed_cpu_jobs={} removed_cpu_waiters={}",
+            keep_track_ids.len(),
+            http_removed,
+            cpu_removed_jobs,
+            cpu_removed_waiters
+        );
+    }
+
+    Ok(AnalysisPrunePendingResult {
+        keep_count: keep_track_ids.len(),
+        http_removed,
+        cpu_removed_jobs,
+        cpu_removed_waiters,
+    })
+}