Access the Floating Workspace from mobile (#8405)

Surface the desktop Floating Workspace (the global, repo-less scratchpad
of terminal tabs under the synthetic `global-floating-terminal` id) on the
mobile app so a Claude session left running there is reachable from a phone.

Adds a terminal-icon button to the mobile host header (phone + tablet
sidebar) that opens the existing Session screen for the floating id. The
sentinel already had host-side RPC support (#5946: local runtime, homedir
cwd, explicit-id fast paths in session.tabs.*); this wires up the mobile
surface and gates it on a new `floatingWorkspaceEnabled` status flag so the
entry hides on hosts that predate it or where the feature is disabled.

The Session screen learns an `isFloatingWorkspaceRoute` flag (mirroring the
existing `folder:` route pattern) that hides repo-backed surfaces — Files,
Source Control, PR/checks, agent history — skips the diff-comment and GitHub
probes, routes terminal URL taps to the phone browser, and limits the New
Tab drawer to terminals + agents (browser/markdown creation resolves a real
worktree host-side and stays desktop-only). useLiveWorktreeName
short-circuits for the sentinel so it no longer polls worktree.show forever.

Extracted the host status.get gating into a useHostStatusGates hook to keep
the host screen under the max-lines ratchet.

src/main/runtime/orca-runtime.test.ts

@@ -1627,6 +1627,19 @@ describe('OrcaRuntimeService', () => {
     expect(runtime.getStatus().terminalWindowsShell).toBe('wsl.exe')
   })
 
+  it('reports floating workspace availability from settings on status', () => {
+    expect(createRuntime().getStatus().floatingWorkspaceEnabled).toBe(true)
+
+    const disabledRuntime = new OrcaRuntimeService({
+      ...store,
+      getSettings: () => ({
+        ...store.getSettings(),
+        floatingTerminalEnabled: false
+      })
+    } as never)
+    expect(disabledRuntime.getStatus().floatingWorkspaceEnabled).toBe(false)
+  })
+
   it('advertises browser screencast only when a renderer window is available', () => {
     const runtime = createRuntime()
     electronMocks.BrowserWindow.fromId.mockReturnValue({ isDestroyed: () => false } as never)

src/main/runtime/orca-runtime.ts

@@ -881,6 +881,7 @@ type RuntimeStore = {
     agentDefaultArgs?: GlobalSettings['agentDefaultArgs']
     agentDefaultEnv?: GlobalSettings['agentDefaultEnv']
     terminalWindowsShell?: GlobalSettings['terminalWindowsShell']
+    floatingTerminalEnabled?: GlobalSettings['floatingTerminalEnabled']
     agentStatusHooksEnabled?: GlobalSettings['agentStatusHooksEnabled']
     defaultTaskSource?: GlobalSettings['defaultTaskSource']
     defaultTaskViewPreset?: GlobalSettings['defaultTaskViewPreset']
@@ -3134,6 +3135,7 @@ export class OrcaRuntimeService {
       capabilities,
       hostPlatform: process.platform,
       terminalWindowsShell: this.store?.getSettings?.().terminalWindowsShell ?? null,
+      floatingWorkspaceEnabled: this.store?.getSettings?.().floatingTerminalEnabled !== false,
       protocolVersion: RUNTIME_PROTOCOL_VERSION,
       minCompatibleMobileVersion: MIN_COMPATIBLE_RUNTIME_CLIENT_VERSION
     }

src/shared/runtime-types.ts

@@ -77,6 +77,9 @@ export type RuntimeStatus = {
   // Why: legacy or saved WebSocket pairings may not carry scope metadata, so
   // the server stamps the authenticated token scope here for status.get only.
   deviceScope?: DeviceScope
+  // Why: mobile gates its Floating Workspace entry on this; absent on older
+  // hosts, false when the user disabled the feature in desktop settings.
+  floatingWorkspaceEnabled?: boolean
   // COMPAT(runtimeStatusMobileAliases): added 2026-05-15 for mobile builds
   // that still read these names; new desktop/CLI code uses the fields above.
   protocolVersion?: number