Polish extensions consistency states

[brsbl]

Summary

• polish full-screen menu, side-chat, new-thread panel, provider filter, and Settings visibility states
• derive the 13-card BB Official catalog from the bundled plugin registry (9 included, 4 optional)
• keep thread headers inside their own columns so controls cannot bleed into the right panel
• add regression coverage for catalog/card parity and thread/right-panel ownership

Verification

• exact branch Electron dev app: plugin catalog top/bottom, provider menu, Settings experiment on/off, new-thread panel, supported tabs, side chat, browser URL chrome, sidebar-tab full screen, and split-thread full screen
• focused @bb/app: 11 files / 127 tests; catalog regression: 5 tests
• @bb/server catalog: 7 tests
• @bb/server-contract: 2 tests
• @bb/sdk: 37 tests
• Turbo typecheck: @bb/app, @bb/server, @bb/plugin-sdk, @bb/templates

Stack parent: #967. Do not merge.