fix(extension): coalesce daemon websocket connects

[jackwener]

Summary

• add a Browser Bridge connect in-flight lock so startup / keepalive / reconnect callers share one daemon connection attempt
• re-check active WebSocket state after async daemon probe and context lookup before constructing a socket
• add a regression test that repeated keepalive calls during the probe produce only one WebSocket

Fixes #1552

Validation

• npx vitest run --project extension extension/src/background.test.ts
• npm --prefix extension run typecheck
• npm --prefix extension run build
• git diff --check