fix(client): preserve inline rename input across tab re-renders (#81)

When the inline session-rename input is open, any incoming SSE event
that triggers renderSessionTabs() (a sibling session updating, a hook
firing, a status change) destroys the input element mid-keystroke and
the user loses what they were typing.

Add a _inlineRenameActive flag that:
- guards the two render paths (renderSessionTabs and
  _fullRenderSessionTabs) so they bail out early while a rename is
  in progress;
- is set true when the inline input mounts (session-ui.js);
- is cleared in finishRename, which then explicitly calls
  renderSessionTabs to restore the normal tab structure.

Also add a re-entrance guard at the top of finishRename so the blur
event and the Enter keydown do not both fire it (was a latent
double-call).

Drive-by: replace tabName.innerHTML = "" with explicit child removal.
The preceding textContent = "" already clears the element; this avoids
an innerHTML write on a node that takes user-supplied content on the
next line.

Follow-up to the inline-rename feature cherry-picked from #60.

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

src/web/public/app.js

@@ -1844,6 +1844,8 @@ class CodemanApp {
   // ═══════════════════════════════════════════════════════════════
 
   renderSessionTabs() {
+    // Don't re-render while user is typing in the inline rename input
+    if (this._inlineRenameActive) return;
     this._debouncedCall('sessionTabs', this._renderSessionTabsImmediate);
   }
 
@@ -1988,6 +1990,7 @@ class CodemanApp {
   }
 
   _fullRenderSessionTabs() {
+    if (this._inlineRenameActive) return;
     const container = this.$('sessionTabs');
 
     // Clean up any orphaned dropdowns before re-rendering