When I go to select download folder for a new torrent, the window is blank and all the "save to" locations are grayed out. This is recent and seems to be since an update to Windows 11 25H2. Is there a workaround for this?

I'll assume you are using the newest version, v3.42. If not upgrade and see if it still happens.
Does it happen if you try to change the location of a torrent? Or with any other pop-up window like those? Does it happen with any other program you run? Since it happened right after a Windows Update I would highly suspect something with the update messed up that window display.

Close Tixati, then right click over Tixati executable from the installation folder, click on Properties, then on Compatibility. Now enable Run this program in compatibility mode for, and finally click on OK.

I noticed this issue for the first time yesterday. Restarting my PC and allowing windows to re-index everything without tixati open for a bit seemed to have at least temporarily resolved the issue.