Perhaps a beginning of answer concerning the fact of receiving the notifications well after having received a message on signal (this day I received a notification two hours after the sending of the message by my signal correspondent).
Go to Settings -> System -> Advanced preferences -> MicroG -> Cloud messaging -> "Three dot menu" -> Advanced
Once here in “Networks to use for push notifications” go to Mobile network : “Ping interval: 60 seconds”
I haven’t had the time to really test if it works and if it consumes more battery than usual but maybe by updating every 60s I’ll get the push notifications on time.
EDIT: seems to work for me on my Samsung S9 v1.1 with advanced privacy for tacker “on”.