CLI and TUI advertise io.modelcontextprotocol/ui although they cannot render MCP Apps

Problem

core/mcp/extensions.ts registers the MCP Apps extension (io.modelcontextprotocol/ui) as advertised by default, on the premise that "the Inspector always renders MCP Apps". InspectorClient applies that default in every client. The web client renders Apps, but the CLI (which has only the --app-info metadata probe) and the TUI cannot, and neither overrides the default.

Servers use the client's extension advertisement to decide whether to return an App. A server talking to the CLI or TUI can therefore send UI those clients cannot consume, which misrepresents the client under test.

Expected

Only a client that can render Apps advertises io.modelcontextprotocol/ui. The CLI and TUI should not advertise it by default. If metadata probing needs the server to believe Apps are supported, that should be an explicit opt-in flag.

Context

Found in Copilot review of #2401. The roadmap's §4 extension table records it as a compatibility gap.

Start in core/mcp/extensions.ts and trace how InspectorClient applies the default extension advertisement to the CLI and TUI. Check the existing --app-info metadata probe and client setup paths. Done means only clients that render MCP Apps advertise io.modelcontextprotocol/ui, with any metadata-probing opt-in explicit.