Hyprland works fine on Nvidia, I've been using it for about a year now. It's only going to improve now that Nvidia hired people from the Nouveau team to work on Nouveau and Nvidia is making the open drivers the default in version 560. Can't wait for the 555 drivers they've been working on with the Wayland team and most of the major desktops to implement explicit sync etc.

An option would be to only install the CUDA toolkit without the drivers but distros like Ubuntu just don't support it. You could also switch display managers to sddm because Hyperland recommends it, might work better. Hyprland prints information in the tty if you launch it with Hyprland. I'm just thinking it's gdm being weird tbh.