feat: reuse warmed model store, add picker timing, and fix discovery error caching

[dgageot]

The model picker pipeline was doing redundant work: each runtime session, server session, and embedded-chat path independently warmed its own models.dev store, even though a single warm copy is sufficient for the lifetime of the process. On top of that, context-cancelled discovery errors were being cached, causing subsequent requests to fail silently, and the picker had no way to understand why discovery was slow or where time was being spent.

This change wires a single shared ModelStore through the CLI entry point (cmd/root/run.go), the app layer, and both the runtime and server session constructors, so the expensive initial fetch happens once and the result is reused everywhere. The model picker now also accepts custom provider references directly, lifting a restriction that forced all providers through the standard discovery path. Timing instrumentation has been added throughout the picker pipeline — from initial store lookup through to final model selection — so latency spikes are visible in debug logs. Finally, context-cancellation errors are no longer cached in the discovery layer; a cancelled lookup leaves the cache empty so the next request retries cleanly.

Validated with task --force lint and task --force test.