fix(core): report tasks running in another Nx process in the inline TUI

[AgentEnder]

Current Behavior

When a task is being run by a different Nx process, this process never gets a pty for it — there is no output to stream and nothing to interact with.

The full-screen terminal pane already handles this: it renders Running in another Nx process... for a task whose status is Shared/Stopped with no pty.

The inline TUI does not. It falls back to Waiting for tasks to start... for any missing pty, without asking why the pty is missing, so:

• A task running in another Nx process shows Waiting for tasks to start... indefinitely — output that will never arrive.
• The user can still enter inline mode for such a task (F11, Enter on a focused pane, double-click a pane, Enter/F11 from the run report), landing in a view that can never render anything.
• A task already displayed inline that transitions from pending (dependency view) to running-elsewhere keeps showing the same misleading message.

Expected Behavior

The two views agree, and inline mode is never a dead end:

• Entering inline mode is blocked for a task another Nx process is running. A hint (This task is running in another Nx process) is shown instead of switching, so the user stays in full-screen where the pane explains what is happening. All four entry points route through a single App::request_inline_mode.
• The inline no-pty fallback is status-aware. A task that is (or becomes) running-elsewhere renders Running in another Nx process..., covering the case where the user was already in the inline TUI when the task transitioned. An in-progress task with no pty renders Waiting for task results..., matching the full-screen pane's wording.
• A new TuiState::is_running_in_another_process (status is Shared/Stopped and no local pty) gives the inline app a single named definition of "running elsewhere" that matches what the full-screen pane checks. The pane still reads its own TerminalPaneState copies rather than calling the helper (it works off flattened props, not TuiState), so the two agree today but are not yet structurally coupled — unifying the pane on the helper is a reasonable follow-up.

Note: the guard applies to a task selected in the task list as well as one pinned to a focused pane — inline always renders exactly one item, and that item would have nothing to show.

Known limitation (inherited, follow-up): because Shared and Stopped are lumped together, a shared continuous task that has finished (goes Stopped, never had a local pty) keeps rendering Running in another Nx process.... The full-screen pane already behaves this way, so this change inherits rather than introduces it.

Tests

• test_inline_mode_blocked_for_task_running_in_another_process — a shared task shows a hint and does not switch.
• test_inline_mode_allowed_for_local_task — a locally running task still drops into inline.
• test_inline_reports_task_running_in_another_process — renders the inline view across the NotStarted → Shared → Stopped transition.

All 320 TUI tests pass; cargo fmt --check and cargo clippy are clean. End-to-end validation against a real second Nx process holding a shared task has not been done — behavior is covered by unit tests.

Related Issue(s)

Relates to NXC-4597

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[AgentEnder]

Rebased onto latest master. The build_status_bar_props conflict from #36263 was purely textual (both PRs appended a method right after dispatch_action); kept both. The full status_bar suite plus the three new tests pass on the rebased tree.

Addressed the two non-blocking notes:

• Rustdoc on is_running_in_another_process — reworded to your suggestion. It now describes the predicate (Shared/Stopped with no local pty) and calls out that the pty check is the load-bearing conjunct separating a task stopped elsewhere from one stopped locally, which does have a pty. You're right that Stopped is terminal and set locally on the fulfilled path in task-orchestrator.ts — the old present-tense 'is being run by' wording didn't fit it.
• 'cannot drift apart' — softened in the description. The pane reads its own TerminalPaneState (flattened props, not TuiState), so it can't call the helper without a larger refactor; the description now says the two agree today but aren't structurally coupled, and flags unifying the pane as a follow-up.

Also captured the finished-shared-task rendering as a known-limitation note in the description for the follow-up.

One clippy nit surfaced by the rebase (collapsible_if in request_inline_mode) is fixed with a let-chain, matching the edition-2024 idiom already used elsewhere in app.rs.

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