Upgrading
Click on Help -> Version to use the button 'Check for Updates'.
If there is a new version available, it will offer to download the AppImage for you. (If you are using pip or poetry, you wouldn't want to use this option, you can use those tools to update your local installations).
After the AppImage is downloaded to your 'Downloads' folder, it will also verify the signature. The GPG public key is baked into the app itself, and (if you want to put it in your keychain or compare it) is the same as the one at https://mig5.net/static/mig5.asc.
If you are not using AppImage, you will need to use pip, git or poetry to update to the new version, depending on how you installed it in the first place.