[Feature Request] Add background process visibility and continuation prompts after execution

Bug Description
i wish claude code would describe the background processes it is running once the prompt is finished, and ask you if you want to continue running. i want to save the context and not have some command running in the background for a long time

Environment Info

• Platform: darwin
• Terminal: vscode
• Version: 2.1.1
• Feedback ID: 83acb949-8d7c-40d1-8ece-e42916592522

Errors

[{"error":"AxiosError: Request failed with status code 401\n    at Xy (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:56:1138)\n    at IncomingMessage.<anonymous> (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:57:9857)\n    at IncomingMessage.emit (node:events:531:35)\n    at IncomingMessage.emit (node:domain:489:12)\n    at endReadableNT (node:internal/streams/readable:1698:12)\n    at process.processTicksAndRejections (node:internal/process/task_queues:90:21)\n    at e$A.request (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:59:2132)\n    at process.processTicksAndRejections (node:internal/process/task_queues:105:5)\n    at async D37 (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:3091:8550)\n    at async file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:3091:9468","timestamp":"2026-01-09T02:57:56.712Z"},{"error":"AxiosError: Request failed with status code 401\n    at Xy (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:56:1138)\n    at IncomingMessage.<anonymous> (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:57:9857)\n    at IncomingMessage.emit (node:events:531:35)\n    at IncomingMessage.emit (node:domain:489:12)\n    at endReadableNT (node:internal/streams/readable:1698:12)\n    at process.processTicksAndRejections (node:internal/process/task_queues:90:21)\n    at e$A.request (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:59:2132)\n    at process.processTicksAndRejections (node:internal/process/task_queues:105:5)\n    at async tKA (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:1840:21167)\n    at async Promise.all (index 0)\n    at async K (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:4061:18091)","timestamp":"2026-01-09T02:57:56.796Z"},{"error":"AxiosError: Request failed with status code 401\n    at Xy (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:56:1138)\n    at IncomingMessage.<anonymous> (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:57:9857)\n    at IncomingMessage.emit (node:events:531:35)\n    at IncomingMessage.emit (node:domain:489:12)\n    at endReadableNT (node:internal/streams/readable:1698:12)\n    at process.processTicksAndRejections (node:internal/process/task_queues:90:21)\n    at e$A.request (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:59:2132)\n    at process.processTicksAndRejections (node:internal/process/task_queues:105:5)\n    at async oY0 (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:1840:21374)","timestamp":"2026-01-09T02:57:56.933Z"},{"error":"AxiosError: Request failed with status code 401\n    at Xy (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:56:1138)\n    at IncomingMessage.<anonymous> (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:57:9857)\n    at IncomingMessage.emit (node:events:531:35)\n    at IncomingMessage.emit (node:domain:489:12)\n    at endReadableNT (node:internal/streams/readable:1698:12)\n    at process.processTicksAndRejections (node:internal/process/task_queues:90:21)\n    at e$A.request (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:59:2132)\n    at process.processTicksAndRejections (node:internal/process/task_queues:105:5)\n    at async e71 (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:1840:21624)\n    at async I (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:4061:18501)","timestamp":"2026-01-09T02:58:12.666Z"},{"error":"lJ1: Another process is currently installing an update\n    at vHA (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:2027:2026)\n    at file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:3060:11013\n    at process.processTicksAndRejections (node:internal/process/task_queues:105:5)","timestamp":"2026-01-09T02:58:13.530Z"},{"error":"lJ1: Another process is currently installing an update\n    at vHA (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:2027:2026)\n    at file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:3060:11013\n    at process.processTicksAndRejections (node:internal/process/task_queues:105:5)","timestamp":"2026-01-09T02:58:16.791Z"},{"error":"Error: Request was aborted.\n    at BP.makeRequest (file:///opt/homebrew/lib/node_modules/@anthropic-ai/claude-code/cli.js:928:3940)\n    at 

Note: Error logs were truncated.