Unless these extensions provide their own action log plugins then this is to be expected

It's only for searching usernames. It's not made clear in J3. In J4 a tooltip is shown:

@brianteeman: As I wrote... the entries I'm speaking off are already logged.

@SharkyKZ: It'd be a lot more useful if all fields were searchable. Is there a reason why the devs have decided against it but to implement a tooltip instead? Ridiculous imo :-) How can I convert this into a feature-wish?

By asking nicely

Absolutely! :-)
But where?

Activities aren’t going to be easily searched. You’ve got language strings in the database to allow messages to be translated and a JSON data structure which generally isn’t going to be good for user searches. Rewriting this system to allow user searches is going to require a massive B/C break in the action log data structure and probably lose some capabilities along the way.

Thx for the explanation which clears things up.

For me though it does render the search more or less half useless. I need to search for a users actions far less often than for actions regarding a specific extension over time.