Improve shinychat integration in btw_app()

[gadenbuie]

Summary

• keep tool selection synchronized with the active shinychat client
• prevent model, prompt, clear, and tool mutations while responses stream
• rely on shinychat's built-in tool cards for collapse, status, fullscreen, and accessible focus management
• preserve rich R output plus per-expression copy and IDE actions through progressive enhancement
• move file actions and full-result "Copy as reprex" into tool-result footers
• remove btw's custom R tool-card, fullscreen, collapse, and icon implementation

Verification

• focused tool-run tests: 116 assertions passed
• GitHub and package-tool consumer tests passed
• R and JavaScript syntax, Air formatting, and diff checks passed
• Chromote verified built-in card rendering, per-block copy, footer reprex copy, and fullscreen entry
• full devtools::test() completed with all feature-relevant tests passing; four unrelated CLI/environment assertions failed around version dispatch and an unset CRAN mirror
• earlier branch-wide R CMD check reached 1,773 passing assertions; three workers failed only because the Pandoc download timed out