The migration from Radix to Base UI broke file attachments because
calling e.preventDefault() in the onClick handler does not stop Base UI
menus from closing. Base UI relies on an internal closeOnClick mechanism
instead. As a result, when the menu closed, the portaled hidden <input
type="file"> elements were unmounted from the DOM before the user could
select a file.
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<!-- This is an auto-generated description by cubic. -->
## Summary by cubic
Fixes the file attachment menu so selecting “Attach chat context” or
“Upload to codebase” no longer closes the dropdown too early. Uses
closeOnClick={false} with direct onClick handlers to keep hidden inputs
mounted and make file selection reliable.

<sup>Written for commit afe8de3b5de300b8c2254418aa9bbd87d818c0bf.
Summary will update on new commits.</sup>

<!-- End of auto-generated description by cubic. -->