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/crates/psysonic-core/src/user_agent.rs

@@ -0,0 +1,26 @@
+//! Process-global outbound User-Agent for Rust-side HTTP.
+//!
+//! Initialised to `psysonic/<version>` (workspace package version) and then
+//! overridden from the main WebView's `navigator.userAgent` once the frontend
+//! reports it during startup. Every Rust HTTP client (`reqwest::Client`,
+//! handcrafted `header::USER_AGENT`) reads the current value via
+//! [`subsonic_wire_user_agent`] so a single switch keeps server-side
+//! request-fingerprints consistent.
+
+use std::sync::{OnceLock, RwLock};
+
+pub fn default_subsonic_wire_user_agent() -> String {
+    format!("psysonic/{}", env!("CARGO_PKG_VERSION"))
+}
+
+pub fn runtime_subsonic_wire_user_agent() -> &'static RwLock<String> {
+    static UA: OnceLock<RwLock<String>> = OnceLock::new();
+    UA.get_or_init(|| RwLock::new(default_subsonic_wire_user_agent()))
+}
+
+pub fn subsonic_wire_user_agent() -> String {
+    runtime_subsonic_wire_user_agent()
+        .read()
+        .map(|ua| ua.clone())
+        .unwrap_or_else(|_| default_subsonic_wire_user_agent())
+}