"Join Site X" sign-up modal is not idempotent when opened via "Add a comment"

Question

This is a very low priority UI bug I discovered accidentally.

To reproduce:

1. Visit a site where you are not logged in.
2. Open any question, click "Add a comment" button below the question or any answer.
3. Observe "Join User Experience" (using that site as an example) modal dialog.
4. Close the dialog (with "x", Esc or by clicking on backdrop).
5. Click "Add a comment" again. Observe no visible changes (no console errors either).

This does not apply to other login-required actions I tested (e.g. "Follow" link opens the modal on every click). This seems to apply to all network sites.

System info: Brave Browser 127.1.69.131 beta (also reproduces on Mozilla Firefox 128.0.3), Ubuntu 22.04 LTS.