feat(onboarding): port first-touch hints to the TUI (#16054)

PR #16046 added /busy and /verbose hints to the classic CLI and the
gateway runner but skipped the Ink TUI (and therefore the dashboard
/chat page, which embeds the TUI via PTY).  This extends the same
latch to the TUI with TUI-native wording.

The TUI's busy-input model is not the /busy knob from the CLI —
single Enter while busy auto-queues, double Enter on an empty line
interrupts.  The new busy-input hint teaches THAT gesture instead of
telling the user to flip a config that does not apply.

Changes:
- agent/onboarding.py — add busy_input_hint_tui() + tool_progress_hint_tui()
- tui_gateway/server.py — onboarding.claim JSON-RPC (Ink triggers busy
  hint on enqueue) + _maybe_emit_onboarding_hint helper hooked into
  _on_tool_complete for the 30s/tool_progress=all path.  Same
  config.yaml latch so each hint fires at most once per install across
  CLI, gateway, and TUI combined.
- ui-tui/src/gatewayTypes.ts — OnboardingClaimResponse + onboarding.hint event
- ui-tui/src/app/createGatewayEventHandler.ts — render the hint event as sys()
- ui-tui/src/app/useSubmission.ts — claim busy_input_prompt on first
  busy enqueue
- tests/agent/test_onboarding.py — +3 cases for TUI hint shape
- tests/tui_gateway/test_protocol.py — +4 cases for onboarding.claim
- website/docs/user-guide/tui.md — new 'Interrupting and queueing'
  section explaining the TUI's double-Enter model and the hints

Validation:
scripts/run_tests.sh tests/agent/test_onboarding.py \
  tests/tui_gateway/test_protocol.py \
  tests/gateway/test_busy_session_ack.py
  -> 66 passed
npm --prefix ui-tui run type-check -> clean
npm --prefix ui-tui run lint       -> clean
npm --prefix ui-tui run build      -> clean

ui-tui/src/app/createGatewayEventHandler.ts

@@ -570,6 +570,17 @@ export function createGatewayEventHandler(ctx: GatewayEventHandlerContext): (ev:
           sys(`error: ${message}`)
           setStatus('ready')
         }
+
+        return
+      case 'onboarding.hint': {
+        const text = String(ev.payload?.text || '').trim()
+
+        if (text) {
+          sys(`(tip) ${text}`)
+        }
+
+        return
+      }
     }
   }
 }

ui-tui/src/app/useSubmission.ts

@@ -3,7 +3,7 @@ import { type MutableRefObject, useCallback, useRef } from 'react'
 import { attachedImageNotice } from '../domain/messages.js'
 import { looksLikeSlashCommand } from '../domain/slash.js'
 import type { GatewayClient } from '../gatewayClient.js'
-import type { InputDetectDropResponse, PromptSubmitResponse, ShellExecResponse } from '../gatewayTypes.js'
+import type { InputDetectDropResponse, OnboardingClaimResponse, PromptSubmitResponse, ShellExecResponse } from '../gatewayTypes.js'
 import { asRpcResult } from '../lib/rpc.js'
 import { hasInterpolation, INTERPOLATION_RE } from '../protocol/interpolation.js'
 import { PASTE_SNIPPET_RE } from '../protocol/paste.js'
@@ -218,6 +218,22 @@ export function useSubmission(opts: UseSubmissionOptions) {
       composerActions.pushHistory(full)
 
       if (getUiState().busy) {
+        // First-touch onboarding: teach the TUI's auto-queue + double-Enter
+        // interrupt pattern the first time the user hits it.  Claim is
+        // atomic server-side (config.yaml latch), shared with CLI + gateway.
+        gw.request<OnboardingClaimResponse>('onboarding.claim', { flag: 'busy_input_prompt' })
+          .then(raw => {
+            const r = asRpcResult<OnboardingClaimResponse>(raw)
+            const text = r?.hint
+
+            if (typeof text === 'string' && text.trim()) {
+              sys(`(tip) ${text.trim()}`)
+            }
+          })
+          .catch(() => {
+            // Onboarding is best-effort — never block the enqueue path.
+          })
+
         return composerActions.enqueue(full)
       }
 
@@ -229,7 +245,7 @@ export function useSubmission(opts: UseSubmissionOptions) {
 
       send(full)
     },
-    [appendMessage, composerActions, composerRefs, interpolate, send, sendQueued, shellExec, slashRef]
+    [appendMessage, composerActions, composerRefs, gw, interpolate, send, sendQueued, shellExec, slashRef, sys]
   )
 
   const submit = useCallback(