Please see this forum topic: BUG macOS: Anki doesn’t launch, opens terminal instead, and see whether the suggestion to run /Applications/Anki.app/Contents/MacOS/launcher in a Terminal window (or one of the other suggestions in that topic) helps you.
Edit: Added:
I note that currently “macOS 12+” is listed on the Anki download page. However, as I understand it, macOS 13 and earlier are no longer supported by Apple. (macOS 13 Ventura moved to “unsupported” status on September 25, 2025, when macOS 26 Tahoe was released.)
Given that Apple itself officially supports only macOS 14+, perhaps Anki might also want to change the download page to say “macOS 14+”?