infs: doctor verifies inference-lsp in the toolchain dir, not the bin/ symlink the editor actually uses

[0xGeorgii]

Follow-up from the comprehensive review of PR #239 (LSP server). Line numbers reference the PR branch at review time.

Severity: major (1), minor (2), nit (3)

1. Doctor verifies the wrong location for inference-lsp (doctor.rs:364): the check tests toolchains/<default>/inference-lsp, but the VS Code resolve chain only uses <INFERENCE_HOME>/bin/inference-lsp (resolve.ts:68) and PATH (whose managed entry is also bin/). States where the binary exists in the toolchain dir but bin/ has no lsp symlink are reachable and likely during rollout:

   • a pre-PR infs installs a toolchain archive (extraction unpacks inference-lsp; old update_symlinks links only infc); the user then upgrades infs — nothing re-runs update_symlinks;
   • new infs install of an already-installed version early-returns without update_symlinks when a default is already set (commands/install.rs).

   In both states infs doctor prints [OK] inference-lsp: Found at .../toolchains/<v>/inference-lsp while the extension fails with "inference-lsp not found (searched .../bin and PATH)". The natural remediation infs install is a no-op ("already installed"); only the non-obvious infs default <v> heals it. Fix: additionally verify paths.symlink_path(binary_with_ext) resolves; if the toolchain bundles the server but the bin/ link is missing/broken, emit a Warning telling the user to run infs default <version> (or repair the link automatically).

2. The "also on PATH" note reports the install's own symlink (doctor.rs:339): infs puts <INFERENCE_HOME>/bin on PATH at first install, and the extension's runDoctor prepends it explicitly — so on every healthy install which("inference-lsp") resolves to the managed symlink itself and the OK line implies a duplicate copy exists. Exclude the managed bin dir from the PATH-copy note.

3. check_inference_lsp hardcodes the binary name (doctor.rs:338 etc.) instead of iterating ToolchainPaths::OPTIONAL_MANAGED_BINARIES; a second optional managed binary would silently get no doctor coverage.