Is 13.3 voltage normal?

See if there is a difference in voltage between engine running vs engine not running. Charging voltage should be 14+.

Sounds likely you need an alternator

Alternator output will vary. It is not always 14v. The PCM will change the output based on load and battery temperature. Threw me for a loop the first time too.

Lot's of things will affect the charging voltage of an alternator, how much load is on the system light headlights, fans etc, engine RPM, temperature and maybe most importantly battery state of charge. If your battery is fully charged or nearly fully charged the charge voltage will be reduced, if your battery is significantly discharged the charge voltage will be at the high end. Too high of a charge voltage when the battery is already charged will boil the battery while too low may not be able to keep up with the load and charge at the same time resulting in the battery losing ground. I would suggest periodically checking your battery SOC after it has rested without any loads for a few hours either by voltage or specific gravity. You may just be seeing the low charge voltage because the new battery is in good shape.
Also by checking at the battery you may see a higher voltage as the Scangauge may be seeing a voltage drop due to loads.

This article explains some of it however it is describing newer more advanced cars for the most part. An old school test to verify alternator charging is to pull up to a wall with headlights on at night and switch off engine, you should see a slight dimming of the headlights when you shut off, if you don't this means the alternator was not charging.
https://www.underhoodservice.com/alternator-testing-correct-voltage/

I have a USB charger that plugs in where the lighter was that has a voltage display on it. Probably not as accurate as a multimeter, but it usually reads anywhere from 13.8 down to 13.1volts with the engine running. If I have everything turned on (AC blower on high, head lights, fog lights, radio, both seat heaters, rear defrost, etc.) it will go down into the 12 volt readings.

Reading with a meter straight from the alternator, I usually get around 13.6 to 13.8.

Doubt it. I think you're fine. Don't fix what's not broken and don't worry about it.

By any chance do you remember what it was before you swapped in the new battery?

I've been struggling with alternator problems and I think I finally have mine licked. I think I burned the rectifier bridge on my current alternator by not running the Jeep around 2k rpm to get max amps...that and it was a rebuilt alternator and it's possible not all the parts were new and that was just ready to go.

Computer does most of the voltage regulation. If anything check all your nuts and bolts and make sure they are tight.

My original alternator problem was probably nothing more than a loose nut.

-Mac