fix(sidebar): keep OMP split-pane status tied to its PTY

[nwparker]

	Files	Added	Deleted	Net
Test	1	$\color{#1a7f37}{\Huge{\mathbf{+}}}$​137	0	$\color{#1a7f37}{\Huge{\mathbf{+}}}$​137
Prod	2	$\color{#1a7f37}{\Huge{\mathbf{+}}}$​111	$\color{#cf222e}{\Huge{\mathbf{−}}}$​26	$\color{#1a7f37}{\Huge{\mathbf{+}}}$​85

ELI5

When a split terminal closes one pane, the remaining panes keep their process IDs, but the terminal's numeric pane IDs can have gaps. Orca used the pane number as if it were still a neat 1, 2, 3 list, so it could put a finished OMP pane's title on its sibling and leave the sidebar showing Running forever.

This change follows each live pane's PTY (the process Orca is actually displaying) back to its stable layout leaf. A completed OMP pane now settles its own sidebar row while a still-running sibling remains Running.

What changed

• Keep the existing dense, parked-tab, and title-matching resolution paths.
• For sparse live PaneManager IDs, map the live slot order to ptyIdsByTabId, then resolve each PTY through terminalLayoutsByTabId.ptyIdsByLeafId.
• Share the sparse-slot resolver with the existing runtime title mapping code.
• Add regressions for parked slots, revealed tabs, nested splits, closed panes, and sparse IDs whose layout order differs from PTY order.

This supersedes the attribution portion of #14702 and addresses #15557. It does not change OMP, hook transport, daemon lifetime, or user-facing title styling.

Verification

All commands ran in the isolated stablyai/orca worktree /private/tmp/orca-15557-fix; /Users/nwparker/projects/oh-my-pi was read-only and was not modified.

• ORCA_BACKGROUND_LAUNCH=1 pnpm test src/renderer/src/components/sidebar/worktree-title-derived-agent-rows.test.ts src/renderer/src/lib/runtime-pane-title-leaf-id.test.ts — 33/33 passed.
• Related sidebar/runtime suites — 62/62 passed.
• pnpm tc:web — passed.
• pnpm run check:code-quality:changed — 0 findings across all changed-file gates.
• git diff --check — passed.
• Commit hooks (oxlint, React Doctor, oxfmt) — passed.

The focused regression drives OMP-compatible spinner/ready titles through the same row projection used by the sidebar and asserts the exact pane keys, provider labels, and idle/working states. This is stronger than a screenshot-only check because it exercises the identity mapping that caused the bug.

Visual proof

No layout or styling changed, so a screenshot would not prove the identity bug. The regression captures the user-visible result: the completed pane is idle, while its OMP sibling remains working after a sparse split/close sequence.

Merge risk / readiness

Low merge risk. Three renderer-only TypeScript files, no wire/schema/provider changes, and no OMP source changes. Existing dense and parked paths remain covered. Ready for review after required CI is green.

Checklist

• ELI5 included
• Focused regression tests included
• OMP source inspected read-only at /Users/nwparker/projects/oh-my-pi
• Typecheck, quality, formatting, and diff checks passed
• Cross-pane behavior verified with sparse IDs and mismatched layout order
• No negative user-facing trade-off identified

[pullfrog]

• Checkout PR fix(sidebar): keep OMP split-pane status tied to its PTY #21671 and read full diff
• Read PR summary snapshot and learnings
• Triage: understand OMP split-pane status / PTY behavior
• Dispatch specialists for unresolved questions
• Aggregate findings and draft review
• Update summary snapshot and submit review

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