A couple of things to clarify if you don't mind.
Emails and Texts are two different things.
You mentioned Aqua Mail. Can you try using Samsung Mail app? Just to verify it's not the app doing something. Samsung used to include their email app as a stock app, but they seemed to have removed it in the past year or so. But you can still add it from the Galaxy Store or Google Play. It's not a bad app. I don't use it because of how it handles account colors that I'm not fond of, but otherwise it's fine.
Texts are different, so what do you use for texts? The stock Samsung Messages app? Google Messages? Something else?
I've used the stock app, but use Textra now. Both my sons use the stock app on their Samsungs, and my wife uses whatever her iPhone 12 has. None of us have issues getting texts immediately.
We are all on AT&T too. We all get our emails at all times too with no delays.
Something else to look at... what type of email service are you using?
Is it...
pop3 - which is not push at all and does only pull when opened?
IMAP - which can be set to push, but can also be set to poll or get only when opened as well?
EAS/Exchange - which is always push?
That may suggest a solution depending on the account type.