I do not experience the behaviour with the cursor, but when a game in fullscreen doesn’t play nice, I move it to the second workspace (with a keybind) and then quickly switch to the first workspace with another keybind. Both are easy to remember and as fast as alt + tab.
Many games with anti-cheat work, a comprehensive list can be found here: https://areweanticheatyet.com/
Anyway, I wouldn’t install a rootkit “anti-cheat” on a Windows machine under any circumstances, but that’s just me.