I've been planning out an online multiplayer game for a while now, and I thought I'd share my ideas. It's a platformer game, so if you're still planning on making a slither-type game this probably won't be very helpful, but I'll put it here anyways.
My idea is for a platformer game where 2-5 players are put in a small level with a few obstacles, and it's a race to get to the finish first. The player can take different paths to try and get to the end first, before the other players, and there are various objects that can be interacted with in different ways.
For the online multiplayer aspect, the player's movement and collisions are entirely local. All of the keyboard inputs and movements the player makes are processed the same way as a traditional single-player game, so there is no lag between inputs and movement for your own player. In a different part of the program, there's a loop that continuously uploads your player's data, and then reads the other players' data. The data includes x and y coordinates, velocity, and other metadata (such as player username and costume). When this data for another player is read, the game immediately updates the corresponding sprite with the coordinates and velocity.
If this was the all for the multiplayer network, the other players' movement would be extremely laggy and the sprites would jump from place to place. I came across this project on KA that is able to predict the future movement of a player by looking at the current velocity and anticipating future collisions. This could be implemented into the game so that when given a player's last known coordinates and velocity, it can project the player's current coordinates and velocity with relative accuracy. Collisions are also predicted. How far the model predicts future movement can be adjusted, so the program could calculate latency between when the data is updated and read, and use this to change the prediction time of the model.
Right now I don't have any proof-of-concept for this, it's just a theory, but I do think it's possible if done correctly.