If you don’t have millions of users every month, a naive approach with a regular Postgres or MariaDB instance will probably handle your logs just fine. If you don’t care about permanently persisting these logs, you could also build something using ETS tables.
If you want something more sophisticated built in Elixir, you could give Plausible a try

Dashbit has some articles on building a homegrown solution - Homemade analytics with Ecto and Elixir - Dashbit Blog, though I just use Plausible (they’re built in Elixir so I’m happy to support!)

Google Analytics not only can be used from client-side, but also from server-side.

Check out Server-Side Tracking in Google Tag Manager. In this way, you don’t store any action in your database, but the online service, just like using client-side tracking.