Drag and drop was broken in GNOME 44 for Qt applications, but it seems a fix has been done and should hopefully be available soon. See https://gitlab.gnome.org/GNOME/mutter/-/issues/2715 and https://bugs.launchpad.net/ubuntu/+source/mutter/+bug/2013235 for relevant bug reports.
In the meantime, you could place templates using the “Insert Template” tool instead. :-)