Fix provider status refresh invariants

[yaacovcorcos]

Summary

• centralize raw provider health to complete client status projection on the server
• route initial config, refresh, auth, install/update mutations, and status streams through the projection
• preserve compatibility with older incomplete status payloads through one bounded client resynchronization
• keep invalid custom executable paths explicit instead of silently replacing them with managed installs
• add Antigravity focus/refresh browser regressions and all-provider projection coverage

Root cause

server.refreshProviders returned raw health snapshots without managed runtime capabilities. The web cache replaced its complete provider status with that incomplete response, so Antigravity lost runtime.canInstall and fell back to the external installation guide.

Verification

• bun run typecheck (9/9 packages)
• changed-file oxlint and oxfmt checks
• provider projection/runtime tests (16 passed)
• provider cache/presentation tests (14 passed)
• provider dialog/focus browser tests (9 passed)
• live localhost verification: Install Antigravity remains available after a real focus refresh
• unsigned macOS arm64 artifact build completed successfully

[yaacovcorcos]

Superseded by #52, which includes this provider-status projection work together with the complete Claude terminal-auth and recovery flow.