Right now you can change the release group a release is in in two separate ways. You can do it via the sidebar which enters a "Change release group" edit, e.g. https://beta.musicbrainz.org/edit/22013364 or you can enter it via the release editor which enters it as part of an "Edit release" edit, e.g. https://beta.musicbrainz.org/edit/21946839

I think we should only have one edit type which handles it and ideally also only one way to do it in the UI. My preference would be to remove the "Change release group" link from the sidebar and the separate pages used for it. They only support the direct search whereas the release editor uses the inline search which can do both.