[Feature Request] Add connection status indicator and last-received timestamp to detect dropped connections

Bug Description
sometimes when my connection drops, claude's ui looks like its working but it is not. I have to interrupt it and send a continue prompt. along these lines - perhaps if there would be a timestamp when claude actually received or did last update that would be helpful to detect these dropoffs

Environment Info

• Platform: darwin
• Terminal: Apple_Terminal
• Version: 2.1.123
• Feedback ID: 72e7cce8-d5a3-4c7c-b061-906af2484797

Errors

[{"error":"Error: NON-FATAL: Lock acquisition failed for /Users/martinrapavy/.local/share/claude/versions/2.1.123 (expected in multi-process scenarios)\n    at x86 (/$bunfs/root/src/entrypoints/cli.js:2769:2177)\n    at Jw8 (/$bunfs/root/src/entrypoints/cli.js:2769:1257)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-04-30T19:27:29.644Z"},{"error":"Error: File does not exist. Note: your current working directory is /Users/martinrapavy/PhpstormProjects/api-v1.\n    at call (/$bunfs/root/src/entrypoints/cli.js:4865:7658)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-05-01T08:27:55.243Z"},{"error":"Error: EACCES: permission denied, mkdir '/Users/martinrapavy3'\n    at async mkdir (/$bunfs/root/src/entrypoints/cli.js:55:594)\n    at async call (/$bunfs/root/src/entrypoints/cli.js:3224:536)\n    at async kE5 (/$bunfs/root/src/entrypoints/cli.js:4191:9506)","timestamp":"2026-05-01T08:55:20.624Z"},{"error":"Error: Request was aborted.\n    at makeRequest (/$bunfs/root/src/entrypoints/cli.js:50:3448)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-05-01T13:13:20.337Z"}]