They also have a set of free public DNS servers with a built in blocklist.

No additional software required at all.

https://adguard.com/en/adguard-dns/overview.html

it quite clearly says:

"Please note that content blocking in Safari operates even when the app is not running"

considering that the free extension is built to block ads in Safari, it seems to be doing this just fine without the app running.

No, I know that. The issue is that the actual app extension itself (which is written in Swift and useful for things like picking elements from the page, etc.) will pretend like it cannot function without the Electron app running. Some more details: https://github.com/AdguardTeam/AdGuardForSafari/issues/84#is...