I have a little bit of experience doing this, but I am by no means an expert on the topic. Over lockdown I made a card game which had LAN capabilities, so I know a bit how it works.
I found, at least for a turn based game, it didnt add too much complexity compared to what it would be if it was local multiplayer game. The way I worked it was to hold a server to contain almost all information about the game, and sync all variables and call functions between/on clients. It took a bit of experimenting, but once it was set up I didn't find it to take too much extra effort.
If you need it, I can try and help if you have any specific questions, the High-level multiplayer tutorial on the godot docs was the one that helped me the most.