Since you are on Apple Silicon, first make sure you downloaded the ARM version of the Stream Deck extension.
Or, even better, simply delete everything and re-download the ARM file and repeat the whole procedure.
- Open the Finder and locate the extension in the Extensions folder.
- Hold down the Control key + click on the extension file, then choose Open from the contextual menu.
- This should flag the extension as exception to your security settings.
- I doble-click it afterwards (just in case, although nothing will happen).
- Start Gig Performer
If this doesn’t work, please check out the link above and proceed with the Security and Privavy settings configuration.