In Wayland you can't use KeepassXC's very cool Auto-Type feature (it's somehow Qt's fault?) but if you installed it as a Flatpak you can go into KDE Settings, search for "Flatpak Permission Settings" and in the settings for KeepassXC under "Advanced" you can disable "Wayland Windowing System" to make it work. Nice!
Using the environment variable QT_QPA_PLATFORM=xcb should do the same thing, but it likely won't fix your problem. These two methods allow KeepassXC to run on X11, which lets it access other X11 apps (running on XWayland), meaning native Wayland apps still won't be able to use auto-complete.
There's probably no way around this for now, as this is due to Wayland's design, which has stricter keyboard access safety, as opposed to X11 which just let all apps read/use the keyboard all the time.
It has to be added to the command when you want to launch it, or added to the .desktop file so it does so automatically. On KDE, it should be as easy as right clicking it on the start menu and clicking "edit application" on the second tab there should be a command field, where you can add the variable at the beginning.
In case this doesn't fix it, your alternatives are copying and pasting passwords or, if your main use for it is in a browser, using the official extension.
Cool, thanks, I'll try that out! Could not get browser integtstion to work, the Firefox-addon didn't see the database (maybe another security/sandbox thing?)
Browser integration works on my machine, which also uses Wayland, so unless you're, say, running Firefox from a flatpak or something, I don't see why it shouldn't work.