Users of a service provided by software running on someone else’s computer and users of software that runs on their own computer are not remotely (no pun intended) the same thing.
The AGPL is plainly a nonfree license. @marcan has documented the other nonsensical requirements it has and how complying with it as written is basically impossible even if you want and intend to.
It was created by anticapitalist zealots who want to conflate use and modification of software (a solo activity) to consumption of a service (an activity that involves others). It fails both logically and legally.
The fact that people regard the AGPL as a free software license is insane to me. It reduces your rights if you plug an ethernet cable in. It’s insane.