The Arch wiki may have some ideas for you - tl;dr is that GDM uses a global dconf db over in /etc/ and this might be the root of your problem (these configs might not get cleaned up with a --purge?) I’m a LightDM user so best I can do to help: https://wiki.archlinux.org/title/GDM#dconf_configuration

Most of them (besides weechat-android and quasseldroid which use bouncers/relays) seem to have fallen out of maintenance; Goguma appears to be currently maintained and updated as a pure standalone client and would be what I’d recommend trying first.