fix(tui): keep the way out on the bar, and make Alt+1..9 actually switch

Four faults, all reported at once, and three of them were mine from the last
two commits.

THE HINT VANISHED. Two independent causes. First, a leaked F1 binding: an
attach whose TUI was killed leaves `F1 -> detach-client` in tmux's root table,
and the claim treated "already bound" as someone else's key, so every later
attach fell back to advertising the tmux chord — the bar stopped saying F1
while F1 still worked. A key already bound to `detach-client` now counts as
ours. Second, width: tmux truncates a status line that overflows and drops the
RIGHT-aligned segment, which is the hint. The strip now gets a budget measured
from the terminal's width minus the hint, and it drops tabs from the far end
until it fits. ⚠️ Measured on VISIBLE columns, not format bytes: `#[reverse]`
costs zero columns, and counting it made a strip that "fitted" still truncate
the hint at 80, 100, 120 and 176 columns on a real terminal.

ALT+N DID NOT SWITCH. On the dashboard, a bare digit meant jump AND ATTACH, and
a terminal sends Alt+N as ESC then N: when those land in separate reads —
routine over SSH — the chord decodes as Escape plus a bare digit, so "switch to
tab 2" threw the user into tab 2's pane. A digit now SELECTS, matching what
Alt+N means in the web UI; Enter is how you go in. Inside a pane the keys never
reached the TUI at all, since tmux owns the terminal, so the attach now binds
Alt+1..9 in tmux's root table to `switch-client` — the strip is usable rather
than decorative. ⚠️ The bar is applied to every session the strip can reach,
each highlighting its own tab: with it on the attached session only, switching
landed the user in a pane with no strip and no way out on screen.

⚠️ The leaked-state sweep was missing `status-position`, so it removed the
marker and left the position behind — and with no marker the leftover no longer
matched, making it permanently unsweepable. Found by diffing every session's
options after a detach.

test/tui/tui-app.test.ts

@@ -161,7 +161,7 @@ describe('footerKeysFor', () => {
   it('advertises only the verbs this build implements', () => {
     const keys = footerKeysFor('list', GLYPHS, { server: true }).join(' ');
     expect(keys).toContain('attach');
-    expect(keys).toContain('1-9 jump');
+    expect(keys).toContain('1-9 switch');
     expect(keys).toContain('n new');
     expect(keys).toContain('p prompt');
     expect(keys).toContain('/ search');
@@ -179,7 +179,7 @@ describe('footerKeysFor', () => {
     expect(keys).toContain('1-9 option');
     // `n` cannot mean two things at once, and denying is what it does here.
     expect(keys).not.toContain('n new');
-    expect(keys).not.toContain('1-9 jump');
+    expect(keys).not.toContain('1-9 switch');
   });
 
   it('sends an idle prompt to the composer instead of offering approve/deny', () => {
@@ -673,6 +673,38 @@ describe('the way out of an attach', () => {
     expect(crowded['status-format[0]']).toContain('#[bold]F1#[nobold] back to the codeman dashboard');
   });
 
+  it('fits the strip to the terminal, measuring VISIBLE columns not format bytes', () => {
+    // The test above only checks the hint is in the format STRING, which it
+    // always was. tmux truncates what it cannot fit and drops the right-aligned
+    // segment, so on a real terminal the hint vanished at every width tested
+    // while that assertion stayed green.
+    const hint = ' F1 back to the codeman dashboard ';
+    for (const cols of [80, 100, 120, 176]) {
+      const bar = buildAttachBanner({
+        oneKey: 'F1',
+        cols,
+        tabs: Array.from({ length: 12 }, (_, i) => ({
+          index: i + 1,
+          label: `w${i + 1}-session-name`,
+          active: i === 1,
+        })),
+      })['status-format[0]'];
+      const visible = bar.replace(/#\[[^\]]*\]/g, '');
+      expect({ cols, fits: visible.length <= cols }).toEqual({ cols, fits: true });
+      expect(visible.length).toBeGreaterThanOrEqual(hint.length);
+    }
+  });
+
+  it('keeps at least one tab even when the hint eats almost the whole bar', () => {
+    const bar = buildAttachBanner({
+      oneKey: 'F1',
+      cols: 40,
+      tabs: [{ index: 1, label: 'w1-case', active: true }],
+    })['status-format[0]'];
+    expect(bar).toContain('1 w1-case');
+    expect(bar).toContain('back to the codeman dashboard');
+  });
+
   it("tells the help overlay how to get back, in the socket's own prefix", () => {
     const keys = helpKeysFor(GLYPHS, { server: true, detach: 'Ctrl+A then d' });
     const detach = keys.find(([key]) => key === 'Ctrl+A then d');