AngWay It depends on the app if it handles push notifications without Play. Whatsapp Threema and Signal work fine without. But MS Teams will not ring. If you rely on that.
Who told you banking apps will not work without Play? This is not true. You could easily test yourself by disabling it or revoking network permission temporarily.
It is true that most banking apps will not have push notifications without Playservices. But I do not feel a need for that. I mean if I want to pay something I will open the banking app manually so the notification will work without play.