F0g I am using Molly with websocket and unrestricted battery and experience none of the sort. On occasion notifications may be delayed a few minutes but I guess this is related to websocket implementation.
I am sorry I can't be of better assistance but if this was happening to me, badly affecting my experience, I would back up all I can and do a factory reset and then reinstall everything starting with properly setting up Play services first and then looking at all possible toggles that may be relevant to apps I am using.