Hey, thanks for the report. This is a known issue with chat in a separate window or in the editor pane on a second monitor.
Try this workaround: after you move chat to a new window, reload that window. Cmd+Shift+P > Developer: Reload Window. This should fix the focus and keyboard issues.
Related threads:
- Agent chat entry incorrect interaction with keyboard
- The input caret stuck at the start of the field and does not advance with chat in editor mode
Let me know if the reload helps.