[ltmoerdani]

Summary

• add Beam-specific reasoning configuration and replay support
• detect repeated or overlong Beam tool-call runs
• recover with a tool-free final-answer turn instead of leaving the chat in a loop
• update metadata, tests, architecture map, changelog, and issue documentation

Verification

• npm test — 567/567 passed
• npm run lint — all 7 checks passed
• npm run test-retry — 9/9 passed
• npm run package — VSIX packaged successfully
• git diff --check — passed

Fixes Beam Free tool-call loop reported in issue documentation.