Google says `DRM_IOCTL_MODE_CREATE_DUMB failed` messages are a bug in webkit2gtk that is fixed in a newer version (4.0-41 googling webkit bugzilla), so I guess you may need to wait for that to get into your distro. Interestingly it works here with 4.0-37 but on Cinnamon not KDE.
Just to confirm those messages are from markdown, first launch Geany from the command line with default configuration by `geany -c /tmp/does_not_exist` and see what messages show, then enable only the markdown plugin and see what messages show[^1], then open a markdown file and see that the `DRM_IOCTL_MODE_CREATE_DUMB` messages show.
Also you could see if the webhelper plugin has the same issues, it uses webkit2gtk as well.
[^1]: ignore the raft of messages when the plugin manager is opened, they are harmless and due to GTK ignoring its own stability guarantees.