feat(rpc): render extension components in the shared host

[code-yeongyu]

Problem

Extension UI degrades in the shared host (RPC mode): component-factory widgets (btw panel, todo-sidebar, prompt-url) trigger the "requires the classic TUI" custom_unsupported warning instead of rendering, and setHeader/setFooter factories are silently dropped (connection-handler.ts).

Ideal state (this PR)

Every extension widget/component renders correctly in the shared host, so the classic-TUI-only warning path is never triggered for built-in components.

• New src/modes/rpc/widget-line-renderer.ts: createLiveComponentRenderer() renders component factories server-side into text lines — synchronous first render, coalesced requestRender, unchanged-output suppression, immediate rerender(), disposal, factory/render fault isolation, global theme pass-through.
• setWidget factory branch now emits the EXISTING additive setWidget lines message (rendered output); the custom_unsupported degradation for widget components is deleted. ctx.ui.custom() keeps its opt-in notice.
• setHeader/setFooter forwarded as new additive extension_ui_request methods carrying rendered lines.
• New additive client->server command set_client_info { width }; per-connection width (default 80) with live rerender on change. Attached interactive clients send width on attach and on SIGWINCH.
• Docs: docs/rpc.md + src/modes/rpc/changes.md updated in the same increment.

Additive-only: a default client that ignores unknown methods and never sends set_client_info sees byte-identical behavior for everything it already used.

TDD / evidence (run on a clean remote box)

• Renderer contract: RED (module missing) -> GREEN 8/8 (test/suite/rpc-widget-line-renderer.test.ts).
• Wiring: RED 10-fail -> GREEN 14/14 (test/rpc-socket-host.test.ts): factory widget renders w:80, header/footer additive methods, ZERO custom_unsupported asserted.
• Width: mutation proof — removing the set_client_info rerender loop fails the pin; restored = 14/14.
• Real-surface QA (scripted, committed driver test/manual-qa/shared-host-widget-qa.mts): real socket host + real todotools builtin over the wire -> rendered todo-sidebar lines, zero custom_unsupported, width-60 rerender. QA-PASS transcript captured.
• Full packages/coding-agent suite + root npm run check on the branch; the only full-suite failures (app-server daemon/stdio) reproduce as box-contention flakes: they pass 68/68 focused on this branch AND on origin/main.

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Summary by cubic

Renders extension component widgets, headers, and footers in the shared RPC host instead of dropping them or showing the custom_unsupported warning. Clients that advertise rendered_components via the new set_client_info command receive factory-rendered text lines; clients that ignore unknown methods see byte-identical behavior.

• setWidget factories render server-side into text lines; the widget custom_unsupported degradation is gone, while ctx.ui.custom() keeps its opt-in notice.
• setHeader and setFooter are new additive extension_ui_request methods; footer factories receive a session-backed footer data provider.
• Width defaults to 80, rerenders live on change, and is forgotten when a connection closes.
• Capability registration is connection-wide, survives additional session opens, and is scoped to socket sessions; closing a session removes only its width, while socket release clears the registration.
• Bindings retain factories when no capable connection remains and recreate renderers and footer providers for later capable joiners.
• Snapshot replay applies the same per-connection capability filter, so late joiners only receive rendered records they opted into.
• Interactive hosts advertise rendered_components, report terminal width with live resize updates, re-register after reconnect, and buffer startup UI events so session-start widgets reach the runtime API before the normal listener is installed.
• Renderer faults are isolated without dropping the connection; recovered renders re-emit even when they match the last successful frame.

^{Written for commit e425816. Summary will update on new commits.}