[Feature Request] Update terminal title bar when context is cleared and new task starts

Bug Description
when context is cleared, and a new task is started it should update the terminal title bar. right now it just reflects the old task. when i have multiple of these terminals open in a tabular fashion, it is difficult to see what task a certain tab is upto because the tab title reflects an old task.

Environment Info

• Platform: darwin
• Terminal: Apple_Terminal
• Version: 2.1.66
• Feedback ID: a5fe80b5-7212-46f4-8695-d1543603b8df

Errors

[{"error":"Error: {\"message\":\"Dropped 6 events: max attempts (8) reached\",\"originalLine\":\"6264\",\"originalColumn\":\"1378\",\"line\":\"6264\",\"column\":\"1378\",\"sourceURL\":\"/$bunfs/root/claude\",\"stack\":\"Error: Dropped 6 events: max attempts (8) reached\\n    at doExport (/$bunfs/root/claude:6264:1378)\\n    at export (/$bunfs/root/claude:6264:887)\\n    at <anonymous> (/$bunfs/root/claude:119:165449)\\n    at <anonymous> (/$bunfs/root/claude:119:165389)\\n    at new Promise (native:1:11)\\n    at EqD (/$bunfs/root/claude:119:165366)\\n    at R (/$bunfs/root/claude:120:17275)\\n    at <anonymous> (/$bunfs/root/claude:120:16548)\\n    at new Promise (native:1:11)\\n    at _flushOneBatch (/$bunfs/root/claude:120:16508)\",\"name\":\"Error\"}\n    at error (/$bunfs/root/claude:2402:25029)\n    at <anonymous> (/$bunfs/root/claude:119:92465)\n    at A4D (/$bunfs/root/claude:119:93009)\n    at <anonymous> (/$bunfs/root/claude:120:17366)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-06T02:35:19.804Z"},{"error":"Error: {\"message\":\"Dropped 6 events: max attempts (8) reached\",\"originalLine\":\"6264\",\"originalColumn\":\"1378\",\"line\":\"6264\",\"column\":\"1378\",\"sourceURL\":\"/$bunfs/root/claude\",\"stack\":\"Error: Dropped 6 events: max attempts (8) reached\\n    at doExport (/$bunfs/root/claude:6264:1378)\\n    at export (/$bunfs/root/claude:6264:887)\\n    at <anonymous> (/$bunfs/root/claude:119:165449)\\n    at <anonymous> (/$bunfs/root/claude:119:165389)\\n    at new Promise (native:1:11)\\n    at EqD (/$bunfs/root/claude:119:165366)\\n    at R (/$bunfs/root/claude:120:17275)\\n    at <anonymous> (/$bunfs/root/claude:120:16548)\\n    at new Promise (native:1:11)\\n    at _flushOneBatch (/$bunfs/root/claude:120:16508)\",\"name\":\"Error\"}\n    at error (/$bunfs/root/claude:2402:25029)\n    at <anonymous> (/$bunfs/root/claude:119:92465)\n    at A4D (/$bunfs/root/claude:119:93009)\n    at <anonymous> (/$bunfs/root/claude:120:17366)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-06T03:05:19.807Z"},{"error":"Error: {\"message\":\"Dropped 6 events: max attempts (8) reached\",\"originalLine\":\"6264\",\"originalColumn\":\"1378\",\"line\":\"6264\",\"column\":\"1378\",\"sourceURL\":\"/$bunfs/root/claude\",\"stack\":\"Error: Dropped 6 events: max attempts (8) reached\\n    at doExport (/$bunfs/root/claude:6264:1378)\\n    at export (/$bunfs/root/claude:6264:887)\\n    at <anonymous> (/$bunfs/root/claude:119:165449)\\n    at <anonymous> (/$bunfs/root/claude:119:165389)\\n    at new Promise (native:1:11)\\n    at EqD (/$bunfs/root/claude:119:165366)\\n    at R (/$bunfs/root/claude:120:17275)\\n    at <anonymous> (/$bunfs/root/claude:120:16548)\\n    at new Promise (native:1:11)\\n    at _flushOneBatch (/$bunfs/root/claude:120:16508)\",\"name\":\"Error\"}\n    at error (/$bunfs/root/claude:2402:25029)\n    at <anonymous> (/$bunfs/root/claude:119:92465)\n    at A4D (/$bunfs/root/claude:119:93009)\n    at <anonymous> (/$bunfs/root/claude:120:17366)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-06T03:35:19.808Z"},{"error":"Error\n    at YM (/$bunfs/root/claude:92:1144)\n    at <anonymous> (/$bunfs/root/claude:93:10067)\n    at emit (node:events:92:22)\n    at endReadableNT (internal:streams/readable:861:50)\n    at processTicksAndRejections (native:7:39)\n    at request (/$bunfs/root/claude:95:2149)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-06T04:05:15.140Z"},{"error":"Error\n    at YM (/$bunfs/root/claude:92:1144)\n    at <anonymous> (/$bunfs/root/claude:93:10067)\n    at emit (node:events:92:22)\n    at endReadableNT (internal:streams/readable:861:50)\n    at processTicksAndRejections (native:7:39)\n    at request (/$bunfs/root/claude:95:2149)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-06T04:05:16.229Z"},{"error":"Error\n  …

Note: Content was truncated.