It is impossible to access the Debug Options screen from the Multiplayer screen, or from inventory GUIs (inventory, chest, beacon…).
Steps to reproduce:
Enter the multiplayer screen or one of the mentioned GUIs
Press f3+f5
Notice how the Debug Options screen doesn’t show up even though it should
They changed the keybind from F5 to F6 in 1.21.9pre4 , so you now can access the screen while on the multiplayer screen without it just refreshing. Seems to just affect inventory GUIs now.