refactor: extract psysonic-syncfs crate (M4/7)

Moves all on-disk cache + device-sync code out of the top crate:

  crates/psysonic-syncfs/                      new lib crate
    src/cache/{offline,hot,downloads,fs_utils} unchanged behaviour
    src/sync/{batch,device}                    (no tray.rs — that's UI)
    src/file_transfer.rs                       shared HTTP helpers
    src/lib.rs                                 + DownloadSemaphore type
                                               + sync_cancel_flags fn

The shell crate keeps `lib_commands/sync/tray.rs` (OS tray icon — UI
concern, will move to shell-tauri at M7) but drops the rest of
`lib_commands/cache/` and the syncfs sibling files.

Tauri command quirk surfaced and resolved: `#[tauri::command]` puts its
`__cmd__*` and `__tauri_command_name_*` helper macros at the *exact*
module of the function, and `pub use` doesn't carry them across module
boundaries. invoke_handler! in lib.rs now references each syncfs
command via its full deepest path
(`psysonic_syncfs::cache::offline::download_track_offline`, etc.) so
Tauri's macros resolve at the right scope. Same approach the audio
crate already uses (`audio::commands::audio_play`).

Cross-crate ref migrations applied via batch sed:
  crate::audio::*               → psysonic_audio::*
  crate::analysis_runtime::*    → psysonic_analysis::analysis_runtime::*
  crate::analysis_cache::*      → psysonic_analysis::analysis_cache::*
  crate::subsonic_wire_user_agent → psysonic_core::user_agent::*
  super::super::file_transfer:: → crate::file_transfer::

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

src-tauri/crates/psysonic-syncfs/src/cache/offline.rs

@@ -0,0 +1,142 @@
+use tauri::Manager;
+
+use psysonic_analysis::analysis_cache;
+use psysonic_analysis::analysis_runtime::enqueue_analysis_seed;
+use crate::DownloadSemaphore;
+
+use crate::file_transfer::{finalize_streamed_download, subsonic_http_client};
+
+// ─── Offline Track Cache ──────────────────────────────────────────────────────
+
+pub async fn enqueue_analysis_seed_from_file(
+    app: &tauri::AppHandle,
+    track_id: &str,
+    file_path: &std::path::Path,
+) {
+    if let Some(cache) = app.try_state::<analysis_cache::AnalysisCache>() {
+        if cache.cpu_seed_redundant_for_track(track_id).unwrap_or(false) {
+            return;
+        }
+    }
+    let bytes = match tokio::fs::read(file_path).await {
+        Ok(v) => v,
+        Err(_) => return,
+    };
+    if bytes.is_empty() {
+        return;
+    }
+    let _ = enqueue_analysis_seed(app, track_id, &bytes).await;
+}
+
+/// Downloads a single track to the app's offline cache directory.
+/// Returns the absolute file path so TypeScript can store it and later
+/// construct a `psysonic-local://<path>` URL for the audio engine.
+#[tauri::command]
+pub async fn download_track_offline(
+    track_id: String,
+    server_id: String,
+    url: String,
+    suffix: String,
+    custom_dir: Option<String>,
+    dl_sem: tauri::State<'_, DownloadSemaphore>,
+    app: tauri::AppHandle,
+) -> Result<String, String> {
+    // Determine base cache directory.
+    let cache_dir = if let Some(ref cd) = custom_dir {
+        let base = std::path::PathBuf::from(cd);
+        // Check that the volume/directory is still accessible.
+        if !base.exists() {
+            return Err("VOLUME_NOT_FOUND".to_string());
+        }
+        base.join(&server_id)
+    } else {
+        app.path()
+            .app_data_dir()
+            .map_err(|e| e.to_string())?
+            .join("psysonic-offline")
+            .join(&server_id)
+    };
+
+    tokio::fs::create_dir_all(&cache_dir)
+        .await
+        .map_err(|e| e.to_string())?;
+
+    let file_path = cache_dir.join(format!("{}.{}", track_id, suffix));
+    let path_str = file_path.to_string_lossy().to_string();
+
+    // Already cached — skip re-download (no semaphore needed).
+    if file_path.exists() {
+        return Ok(path_str);
+    }
+
+    // Acquire a download slot. The permit is held for the duration of the HTTP transfer
+    // and released automatically when this function returns (success or error).
+    let _permit = dl_sem.acquire().await.map_err(|e| e.to_string())?;
+
+    let client = subsonic_http_client(std::time::Duration::from_secs(120))?;
+
+    let response = client.get(&url).send().await.map_err(|e| e.to_string())?;
+    if !response.status().is_success() {
+        return Err(format!("HTTP {}", response.status().as_u16()));
+    }
+
+    let part_path = file_path.with_extension(format!("{suffix}.part"));
+    finalize_streamed_download(response, &file_path, &part_path).await?;
+
+    enqueue_analysis_seed_from_file(&app, &track_id, &file_path).await;
+
+    Ok(path_str)
+}
+
+/// Returns the total size in bytes of all files in the offline cache directory (and optional custom dir).
+#[tauri::command]
+pub async fn get_offline_cache_size(custom_dir: Option<String>, app: tauri::AppHandle) -> u64 {
+    let default_dir = match app.path().app_data_dir() {
+        Ok(d) => d.join("psysonic-offline"),
+        Err(_) => return 0,
+    };
+    let mut total = super::fs_utils::dir_size_recursive(&default_dir);
+
+    if let Some(cd) = custom_dir {
+        let custom = std::path::PathBuf::from(cd);
+        if custom != std::path::PathBuf::from("") {
+            total += super::fs_utils::dir_size_recursive(&custom);
+        }
+    }
+    total
+}
+
+/// Removes a cached track from the offline cache. Accepts the full local path
+/// (stored in OfflineTrackMeta) so it works regardless of which directory was used.
+/// After deleting the file, empty parent directories up to (but not including)
+/// `base_dir` are pruned using `remove_dir` (never `remove_dir_all`).
+#[tauri::command]
+pub async fn delete_offline_track(
+    local_path: String,
+    base_dir: Option<String>,
+    app: tauri::AppHandle,
+) -> Result<(), String> {
+    let file_path = std::path::PathBuf::from(&local_path);
+    if file_path.exists() {
+        tokio::fs::remove_file(&file_path)
+            .await
+            .map_err(|e| e.to_string())?;
+    }
+
+    // Determine the safe boundary — never delete at or above this directory.
+    let boundary = if let Some(bd) = base_dir.filter(|s| !s.is_empty()) {
+        std::path::PathBuf::from(bd)
+    } else {
+        app.path()
+            .app_data_dir()
+            .map_err(|e| e.to_string())?
+            .join("psysonic-offline")
+    };
+
+    if let Some(parent) = file_path.parent() {
+        super::fs_utils::prune_empty_dirs_up_to(parent, &boundary);
+    }
+
+    Ok(())
+}
+