So I've only done some initial investigating into Godot's networking and I can tell you it does 'work' but you're absolutely right to question how useful it will be since for me it's a relatively unknown engine compared to unity or unreal. One thing I have noticed already though is it is much easier to find information on it and get the initial setup done, I haven't though tested out properly whether or not how the networking handles things like hosting which I would like to try but maybe more experienced people who have experimented with Godot could comment on that.
If you do go with Godot, you're probably going to have to learn all about server hosting and so on yourself because of how Godot does not have any kind of third party services for multiplayer the way unity and unreal does so that's something you need to take into account. On the flip side though from what I've seen so far if you don't mind giving out external I.P addresses for people to connect to your game you can pretty much get everything set up yourself and working.
https://godotforums.org/discussion/comment/47916#Comment_47916
See this thread I made on the topic asking about this very thing, the people responding gave some pretty helpful information on it. By all means someone correct me if I'm wrong but in theory I think with the way Godot is setup by default you could probably host a game on your own server, give out the external I.P address of that machine and people will be able to connect if they have the same client and the game is running. It seems to run very much in the old school way like with Minecraft for example where you just directly connect to an I.P address rather than going through a server browser.
Bearing in mind I'm brand new to this too and still doing my own research and experimenting, I plan on getting an ultra simple 'game' set up where you can just move people about and shoot in 2D and see if I can get people to connect to an I.P address based on that. I think that's potentially where someone serious about using Godot for multiplayer should get started, just seeing if people can connect to your game from other devices.
Another example would be the way the old school Freelancer space sim game is setup now, to get around the issue of there being no multiplayer anymore players simply setup their own 'global server list' and so on which you could connect to using the I.P address provided, that would then let people make games on that server and then the list of games would pop up like the game had never died.