Currently previous versions of targets are deleted as the new one is created. This creates a situation where the repo is invalid until snapshot is updated.
Try to leave the old files in place, and only remove them during the snapshot update. This way the target update can be merged and the repo is valid while snapshot is getting updated.
tufrepo verify must be able to handle this and should recognise the issue ("the repo is valid but there are metadata files that are not included in snapshot")