You will find Bartender 4.dmg in your downloads folder. Please open this then move Bartender to your Applications folder and launch it from there.
This download is both the trial and the full version (with license).
You can use the trial as long as its in Public Beta, then for 4 weeks, after this you must purchase a license to unlock the full version.
With version 4.0.20 Bartender 4 now has native support for Apple Silicon.