fix(terminal): address re-review findings on the pane-buffer rework

Follow-up to the PR #112 re-review (all six prior blockers were already
resolved; these are new issues the rework introduced):

- app.js: define the missing `_scheduleTerminalRepaint()` helper. It was
  called from both WebGL-fallback paths (onContextLoss + long-task trip)
  but defined nowhere, so each fallback threw `TypeError` and lost the
  post-fallback repaint, leaving a stale/blank terminal. Implemented as an
  rAF-debounced full refresh (matches the old inline `terminal.refresh`).
- app.js: clear terminal load-state on the two post-write stale-select
  early-returns (cached-buffer + rewrite branches), matching the other
  four checks. Switching away from a mid-loading tab no longer leaks a
  permanent `.tab-loading` spinner / `aria-busy=true`.
- terminal-ui.js + app.js: gate the post-resize TUI-redraw settle on an
  actual dimension change. `sendResize` now returns whether dims changed;
  a same-size tab switch sends no SIGWINCH, so the wait is skipped instead
  of charging a flat tax on every non-shell switch. Literal hoisted to
  `TUI_REDRAW_SETTLE_MS`.
- tmux-manager.ts: `resizeWindow()` uses a non-blocking `exec` instead of
  `execSync` so the interactive WS/HTTP resize path can't stall the
  Fastify event loop on a slow/hung tmux. Sole caller already fire-and-
  forgets the result; test updated to assert the async dispatch.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/web/public/terminal-ui.js

@@ -1906,7 +1906,13 @@ Object.assign(CodemanApp.prototype, {
     // terminal size matches what we report to the server PTY.
     if (this.fitAddon) this.fitAddon.fit();
     const dims = this.getTerminalDimensions();
-    if (!dims) return;
+    if (!dims) return false;
+    // Did the dimensions actually change since the last resize we sent? Callers
+    // use this to skip work (e.g. the post-resize TUI-redraw settle) when no
+    // real SIGWINCH was triggered — switching tabs at the same browser size is
+    // a no-op on the server and needs no redraw grace.
+    const prev = this._lastResizeDims;
+    const changed = !prev || prev.cols !== dims.cols || prev.rows !== dims.rows;
     // Update _lastResizeDims so the throttledResize handler won't redundantly
     // clear the terminal for the same dimensions (which would blank the screen
     // without a subsequent Ink redraw to repaint it).
@@ -1915,7 +1921,7 @@ Object.assign(CodemanApp.prototype, {
     if (!options.forceHttp && this._wsReady && this._wsSessionId === sessionId) {
       try {
         this._ws.send(JSON.stringify({ t: 'z', c: dims.cols, r: dims.rows }));
-        return;
+        return changed;
       } catch {
         // Fall through to HTTP POST
       }
@@ -1925,6 +1931,7 @@ Object.assign(CodemanApp.prototype, {
       headers: { 'Content-Type': 'application/json' },
       body: JSON.stringify(dims),
     });
+    return changed;
   },
 
   /**