refactor: extract psysonic-analysis crate (M2/7)

Moves analysis_cache + analysis_runtime out of the top crate into a new
psysonic-analysis crate, plus the runtime user-agent facade into
psysonic-core. The audio↔analysis dependency cycle is broken via a
PlaybackQueryHandle port registered as Tauri State.

  crates/psysonic-analysis/                new lib crate
    src/analysis_cache/{mod,store,compute} unchanged behaviour
    src/analysis_runtime.rs                + enqueue_analysis_seed (was
                                           in lib_commands/cache/offline)

  crates/psysonic-core/src/
    user_agent.rs                          subsonic_wire_user_agent +
                                           runtime/default helpers
                                           (was in top lib.rs)
    ports.rs                               PlaybackQueryHandle: closure
                                           wrapper, not Arc<dyn Trait>,
                                           so existing State<AudioEngine>
                                           callsites stay unchanged

The shell setup hook registers the real PlaybackQueryHandle once the
AppHandle is available; the closure captures it and re-resolves
AudioEngine via try_state at each call.

Top crate keeps `crate::analysis_cache`, `crate::analysis_runtime`,
`crate::subsonic_wire_user_agent`, and `crate::submit_analysis_cpu_seed`
working via re-exports — no audio/lib_commands callsite needed editing.

Behaviour preserving. Cargo check + clippy --workspace clean (only
pre-existing warnings carry over).

src-tauri/src/lib_commands/cache/hot.rs

@@ -1,9 +1,10 @@
+use crate::analysis_runtime::enqueue_analysis_seed;
 use crate::audio;
 use crate::subsonic_wire_user_agent;
 
 use super::super::file_transfer::stream_to_file;
 use super::downloads::{resolve_hot_cache_root, HotCacheDownloadResult};
-use super::offline::{enqueue_analysis_seed, enqueue_analysis_seed_from_file};
+use super::offline::enqueue_analysis_seed_from_file;
 
 #[tauri::command]
 pub(crate) async fn download_track_hot_cache(

src-tauri/src/lib_commands/cache/mod.rs

@@ -15,5 +15,3 @@ pub(crate) use downloads::{
     check_arch_linux, download_update, download_zip, fetch_netease_lyrics, get_embedded_lyrics,
     open_folder,
 };
-// Internal helper consumed by analysis_runtime (used as analysis_runtime depends on it):
-pub(crate) use offline::enqueue_analysis_seed;

src-tauri/src/lib_commands/cache/offline.rs

@@ -1,44 +1,13 @@
 use tauri::Manager;
 
 use crate::analysis_cache;
-use crate::analysis_runtime::{analysis_backfill_is_current_track, submit_analysis_cpu_seed};
+use crate::analysis_runtime::enqueue_analysis_seed;
 use crate::DownloadSemaphore;
 
 use super::super::file_transfer::{finalize_streamed_download, subsonic_http_client};
 
 // ─── Offline Track Cache ──────────────────────────────────────────────────────
 
-pub(crate) async fn enqueue_analysis_seed(app: &tauri::AppHandle, track_id: &str, bytes: &[u8]) -> Result<bool, String> {
-    if let Some(cache) = app.try_state::<analysis_cache::AnalysisCache>() {
-        if cache.cpu_seed_redundant_for_track(track_id).unwrap_or(false) {
-            return Ok(true);
-        }
-    }
-    let high = analysis_backfill_is_current_track(app, track_id);
-    let outcome = submit_analysis_cpu_seed(
-        app.clone(),
-        track_id.to_string(),
-        bytes.to_vec(),
-        high,
-    )
-    .await
-    .map_err(|e| {
-        crate::app_eprintln!("[analysis] failed to seed {}: {}", track_id, e);
-        e
-    })?;
-    let has_loudness = app
-        .try_state::<analysis_cache::AnalysisCache>()
-        .and_then(|cache| cache.get_latest_loudness_for_track(track_id).ok().flatten())
-        .is_some();
-    crate::app_deprintln!(
-        "[analysis] seed result track_id={} bytes={} has_loudness={} outcome={outcome:?}",
-        track_id,
-        bytes.len(),
-        has_loudness
-    );
-    Ok(has_loudness)
-}
-
 pub(crate) async fn enqueue_analysis_seed_from_file(
     app: &tauri::AppHandle,
     track_id: &str,