what do you have in ~/.profile ?
https://wiki.archlinux.org/title/sway#No_visible_cursor
you can try
copy /etc/sway/config.d/50-systemd-user.conf to $home$/.config/sway/config.d
and make in ~/.config/environment.d/30-envars.conf some environmental as last resort…but …
would check this : Sway with Nvidia Tutorial