This is because the `NODE_OT_group_edit` operator reuses the last value
of the `Exit` property and once this is set it would always try to pop
(instead of push [which is what we want from the icon]) the nodegroup.
Callers of the operator set `Exit` explicitly elsewhere (just not
from node drawing -- where the way it is called [via a more general
callback] makes it difficult to set operator properties from there).
Solve by not saving the property for following usages (flag
`PROP_SKIP_SAVE`).
Fixes#117530.
Philipp Oeser