[Feature Request] Display session name in statusline for multi-instance identification

Bug Description
i want to see the session name in my statusline, i am always running multiple instances and i name each session and it would make it a lot easier to know which session i am working with.

Environment Info

• Platform: darwin
• Terminal: iTerm.app
• Version: 2.0.76
• Feedback ID: 5fb6501f-7b33-4baf-a6a2-a822aa5808d9

Errors

[{"error":"Error: Request was aborted.\n    at _createMessage (/$bunfs/root/claude:458:3157)\n    at processTicksAndRejections (native:7:39)","timestamp":"2025-12-31T21:53:21.511Z"},{"error":"Error: Request was aborted.\n    at makeRequest (/$bunfs/root/claude:801:3940)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-01T23:35:36.365Z"},{"error":"Error: Request was aborted.\n    at _createMessage (/$bunfs/root/claude:458:3157)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T00:22:57.408Z"},{"error":"Error: Request was aborted.\n    at makeRequest (/$bunfs/root/claude:801:3940)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T01:21:20.426Z"},{"error":"Error: Request was aborted.\n    at makeRequest (/$bunfs/root/claude:801:3940)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T02:06:06.210Z"},{"error":"Error: Request was aborted.\n    at _createMessage (/$bunfs/root/claude:458:3157)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T02:06:30.546Z"},{"error":"Error: Request was aborted.\n    at _createMessage (/$bunfs/root/claude:458:3157)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T10:51:50.845Z"},{"error":"Error: Request was aborted.\n    at makeRequest (/$bunfs/root/claude:801:3940)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T11:17:34.735Z"},{"error":"Error: Request was aborted.\n    at _createMessage (/$bunfs/root/claude:458:3157)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T11:22:11.296Z"},{"error":"Error: Request was aborted.\n    at _createMessage (/$bunfs/root/claude:458:3157)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T11:27:45.493Z"},{"error":"Error: EISDIR: illegal operation on a directory, read\n    at readFileSync (unknown)\n    at <anonymous> (/$bunfs/root/claude:12:500)\n    at sW (/$bunfs/root/claude:11:8463)\n    at readFileSync (/$bunfs/root/claude:12:465)\n    at Dw_ (/$bunfs/root/claude:4697:22559)\n    at call (/$bunfs/root/claude:966:945)\n    at call (/$bunfs/root/claude:962:6251)\n    at Qo7 (/$bunfs/root/claude:2142:17437)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T11:46:06.871Z"},{"error":"Error: Request was aborted.\n    at makeRequest (/$bunfs/root/claude:801:3940)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T12:14:27.299Z"},{"error":"Error: Request was aborted.\n    at makeRequest (/$bunfs/root/claude:801:3940)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T12:31:42.571Z"},{"error":"Error: EISDIR: illegal operation on a directory, read\n    at readFileSync (unknown)\n    at <anonymous> (/$bunfs/root/claude:12:500)\n    at sW (/$bunfs/root/claude:11:8463)\n    at readFileSync (/$bunfs/root/claude:12:465)\n    at Dw_ (/$bunfs/root/claude:4697:22559)\n    at call (/$bunfs/root/claude:966:945)\n    at call (/$bunfs/root/claude:962:6251)\n    at Qo7 (/$bunfs/root/claude:2142:17437)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-02T12:56:45.913Z"},{"error":"Error: Request was aborted.\n    at _createMessage (/$bunfs/root/claude:458:3157)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-03T00:55:30.989Z"},{"error":"Error: Request was aborted.\n    at _createMessage (/$bunfs/root/claude:458:3157)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-03T14:17:13.814Z"},{"error":"Error: Request was aborted.\n    at makeRequest (/$bunfs/root/claude:801:3940)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-03T20:54:07.512Z"}]