fix(tui): stabilize Windows terminal snapshots

Treat an absolute path.relative() result as a cross-volume path instead of incorrectly abbreviating it beneath the user's home directory.

Allow embeddings to project a logical footer cwd without changing the operational session cwd. The recorded-session harness now uses a POSIX-shaped display alias for both the footer and filesystem result paths, preserving the existing pre-normalization layout width on every host.

Keep runtime-provided labels behind terminal-control escaping, cover that boundary, and document the embedding contract.

packages/ui/tui/tests/tui.spec.ts

@@ -364,6 +364,13 @@ describe('pi-tui chat lifecycle and transcript', () => {
     const outsideResult = await setup({ cwd: '/opt' })
     expect(outsideResult.terminal.output).toContain('/opt')
     await dispose(outsideResult)
+
+    const logicalResult = await setup({
+      cwd: '/host/worktree',
+      formatCwd: cwd => `logical:${cwd}\x1b`,
+    })
+    expect(logicalResult.terminal.output).toContain('logical:/host/worktree\\x1b')
+    await dispose(logicalResult)
   })
 
   it('sends, steers, handles commands, global keys, and disposed-agent input', async () => {