This issue appears to have been resolved in 26.3-snapshot-4.
Input methods now work on major Linux operating systems, such as Ubuntu 26.04.
Prism Launcher can be made to behave like the official launcher by manually defining the $XMODIFIERS environment variable.
This itself is a bug that should be fixed on the Prism Launcher side.
I can confirm this issue on Ubuntu 26.04 (GNOME on Wayland) and Linux Mint 22.3 (Cinnamon on X11) as well.
I suspect this is an issue affecting all Linux systems.
If it cannot be easily fixed, a note should be added to tooltips or similar locations stating that “Linux is not supported” before the release.