How do I get good cellular service on iPhone with AT&T?

What model phone?

5G? 5G+? LTE? 5Ge?

What about on your old Android?

Are you actually experiencing problems? Dropped calls? No service? Slow data speeds?

The bars don't actually have any actual clearly defined meaning... People think they do, but they don't...

Not beyond a very vague and undefined measure of 'signal strength'... The bars displayed may vary from one model phone to another even though both have the exact same signal and neither one experiences problems.

See the article linked to above by Johnathan Burger.

That would be entirely relative to how well you are receiving a signal on your phone from an AT&T tower. It could be that AT&T doesn't have strong service in your area.

However, if this is a constant wherever you go, there may be an underlying hardware issue with the antennas in your phone.

Yes. Go to an area with better coverage.

Hmmm … you said:

• “Brand new iPhone 16 Pro Max”
• ”All I did was switch my [SIM] to my i[P]hone.”

The iPhone 16 Pro Max sold in the U.S. does not have a SIM card slot. Did you switch an eSIM?

https://www.slashgear.com/948346/the-big-myth-about-cell-signal-you-should-stop-believing/

Follow Johnathan Burger’s advice.