[Bug] Background task output files grow unbounded and can fill disk

Bug Description
Background task output files grow without limit and can fill the disk.

What happened: On Windows, a background task (a Python REPL-style task started from a Claude Code session) wrote its output to a file under %TEMP%\claude\<project>\<session>\tasks\<id>.output. The file was last written 9/30 at 7:12 AM Pacific and was 17,037,249,025 bytes (about 17 GB). Four other .output files from 9/30-10/1 reached 1.8-2.3 GB each, about 25 GB in total. None were still growing when found.

Impact: On 10/6 the C: drive had 0 to 4.6 GB free out of 475 GB. Work stopped until I deleted the logs.

Ask: Please cap the size of background task output files (or rotate/truncate them), warn when one passes a limit, and stop or clean up tasks whose output keeps growing.

Environment Info

• Platform: win32
• Terminal: windows-terminal
• Version: 2.1.291
• Feedback ID: ff852756-6a1d-4b20-a781-6d82d57f376f