Your old Mac had an Intel CPU and your new MacBook Air is Apple Silicon, correct?
Please run the Anki launcher via the /Applications/Anki.app/Contents/MacOS/launcher command in the Terminal app. Doing so will allow you to view any error messages that might get printed.
However, if you know for a fact that the Anki previously installed on your system is intended for Intel-CPU Macs and is now wrong for your Apple Silicon Mac, it is likely that you’ll want to delete the current Anki installation (the ~/Library/Application Support/AnkiProgramFiles directory) and then re-download/re-install Anki to get the version that runs on Apple Silicon. (Your decks, media files, study history, etc. are in a different directory and will not be affected by deleting the AnkiProgramFiles directory. Please see the documentation for more information about the different places user files and program files are stored.)
If you continue to have issues, please provide the error messages you see when running the launcher from the Terminal app.
Another alternative you might want to consider trying would be installing the Anki 26.05 Beta 1 being tested right now. It uses a different installer (a regular .dmg file). I suspect that installing Anki this way would replace the old Anki installation with the new one, fixing the problem of having an incorrect, old version of Anki. However, I’m not sure about this, and that particular situation/scenario hasn’t yet been tested.