Opening SideMini, which is not on the App Store

What you should see

On first launch macOS says the app was downloaded from the internet and asks whether to open it. Click Open. That prompt appears once, for any app from any developer, including notarized ones.

If instead macOS says the developer cannot be verified or the app is damaged, you did not get the app from this site. Delete it and download again from the download page.

What notarization means

Before release, the app is uploaded to Apple, scanned for malicious code and stapled with a ticket macOS checks at launch. It is not the App Store review process and Apple does not inspect what the app does; it is a malware check with a paper trail tied to a real developer account.

Why the App Store is not possible

Sandboxed apps cannot talk to the Sidecar interfaces, cannot create a display, and cannot change energy settings. Every app of this kind, including the free ones, ships outside the store for the same reason.