I want to do the main things like the Colosseum, Vatican museum, St Peter's basilica, Roman forum, etc, but I'm not sure what other gems are out there that are worth the short time I have. I wish I could spend more time there, but alas, this is how the schedule worked out! If this helps any, I don't really care for places like the Spanish Steps. While iconic and beautiful, I want sites where I can really dive into the history of the Roman Empire, especially during/around the Pax Romana. Thank you so much for any advice and suggestions!
Do you have a good guidebook?
If not here is a start
At a Glance
https://www.ricksteves.com/europe/italy/rome
Rome is layers upon layers of history
The Pantheon, the Capitoline museum and the view of the forum from its balcony (made more sense to me than being down in the forum itself), and, while it's not ancient Rome, the Etruscan museum. Oh, and I would hope you could squeeze in a half-day visit to Ostia Antica if you can get an early start. I would skip St. Peter's on such a short trip if you are focussing on ancient Rome.
It's now possible to book an entry reservation for St. Peter's online, which moves you out of the general security line and into a shorter line for those with said reservations. That will make St. Peter's easier to fit into a short visit, unless you are already planning to take one of the commercial tours that combines the Vatican Museums with St. Peter's and is able to move you directly between the two.
If the timing fits, I would recommend Domus Aurea. Are you familiar with it? I’m not sure of current availability as it’s an active archeological site, but I think it would be especially fascinating given your interest.
As a history lover, you could spend weeks--months--in Rome and not exhaust things to see and do. You will have to be very selective.
In addition to the sites mentioned above, you will probably want to see at least the Portico d'Ottavia (and surrounding ruins) and the Ara Pacis (does not take long and which is having a cool evening exhibition now, that we plan to see in a few months: https://www.arapacis.it/).
Usually remarkably uncrowded and just fantastic if you have time, especially the painted garden from the Villa of Livia: National Roman Museum - Palazzo Massimo alle Terme + nearby Baths of Diocletian.