@Mr_NutterButter People still use Quake engines. ioquake3 is a modified Quake III engine that is used in a lot of open-source games. And modified versions of the Quake III engine are still used in the Call of Duty series.
https://ioquake3.org/
Though, I don't know how it would work out for something like Godot. People only modified engines like Quake out of necessity. Something like Godot is more general purpose while the Quake engines were designed more for first-person shooters. Though engines like Quake can be configured to have a third-person camera without modifications (either through scripting or a configuration file), they were still developed with FPS games in mind. I don't know that many games using a modified version of Godot. It seems like it suits every purpose.
Also, not that many people open source their engines anymore. iD stopped open-sourcing their engines (including their legacy engines) after being bought out by Bethesda. Valve and Epic Games never open-sourced any of their engines. Instead, everyone is going for the "source-available" model where you can obtain access to the source code with certain license restrictions, if you pay premium.