m3u_plus files has the function to create your own channel groups/lists.
I've only tried it with Kodi and PVR Simple Client, and it works as it's supposed to. But I have the link to the m3u-file as a source and local caching of the m3u-file disabled. And it still works!
Is the added group settings saved somewhere locally, or is the new group and its settings sent back to the providers servers and stored there?
PVR Simple Client has the function to create your own groups, not the m3u file. PVR Simple Client stores these settings locally.
m3u_plus is just a normal m3u file but it has all the extra info like provider group names, epg tags, etc. When using an m3u link none of your settings are ever sent back to the provider, that functionality just isn't there.