fix(web): keep ineligible message forks disabled

apps/web/tests/snapshots/code-mode-round/ui.expected.md

@@ -7,6 +7,9 @@
 - text: "Using ONE run_code program: run bash `echo CODE_ROUND_OK`, then read the file missing.txt catching its error in the program. Return an object with both outcomes. Then reply DONE and stop. {{clock}}"
 - button "Copy":
   - img
+- button "Branch into a new conversation" [disabled]:
+  - img
+- text: Available only on the last message of a completed turn
 - button "Context injection":
   - img
   - img