Cursor-ide-browser connected but exposes zero tools (browser_tabs/browser_navigate tool not found)

Update from Cursor 3.13.21 (Darwin arm64): still seeing MCP server "cursor-ide-browser" not found / catalog-vs-runtime split, plus adjacent Browser Automation issues.

Filed separate Bug Reports (with cross-links) for the distinct symptoms:

Also related (closed, cannot comment): Cursor-ide-browser MCP disconnects every ~5 minutes during heavy agent browser usage (mid-session lease / “server does not exist”).