The message "You do not have permission to open the application" is shown when trying to open a downloaded app
In playing with the Triangulator app I found the following issues on Big Sur:

When decompressing the .zip, the application contents didn't retain the execute bits.  Add it back with sudo chmod -R 755 /path/to/app.
Since the application was downloaded by a web browser (in my case) the quarantine bits are set on the decompressed files.  Remove that with sudo xattr -dr com.apple.quarantine /path/to/app.

Once those issues are remediated then the application can be launched.
-Eric