Paradises connect to BT classic using two protocols, one is for calls and another is for streaming. The second one is the one which is triggered by all notifications as well (even if notification is silent, it might trigger the stream but send nothing, however aids will switch between where they were and that stream nevertheless).
Solution for uninterrupted stream is to on the device you sent want to send notifications to turn off streaming part of BT on that device (but leave calls if you want). Afaik iphones can do that.
Or if you know that you don’t want anything from phone coming in while you’re on ipad, just turn off BT on the phone (or just HA connection as a whole) and when you’re done with ‘no interruptions’, you turn on BT on the phone again.
Again, just simple connect/disconnect, no unpairing/forgetting or similar.