I wrote this review to provide a brief overview of what visitors can currently expect from Aigai (September 2023). Most importantly, the palace site is still closed for construction works, the re-opening date is not known. The theatre is open to visitors, but there is not much to see (nothing more than on the photo in Solivagant's review). The new museum is open (since December 2022). And as mentioned in the previous review, photography is now allowed (without flash) in the Royal Tombs Museum.
[Edit January 2024: the Palace of Aigai was reopened on January 7, 2024]

Here is my dialogue with the lady at the ticket counter at the Royal Tombs:
Lady: Would you like to take a combined ticket?
Me: What is included?
Lady: The Royal Tombs museum, the new museum outside the town and the archaeological park.
Me: Archaeological park? Is that the site where the palace and the theatre are?
Lady: The palace is closed for construction work.
Me: Do you know when it will reopen?
Lady: They said at the end of the year. So maybe next year. Maybe (accompanied by a shrug of the shoulders).
Me: And what about the other tombs that are even marked on Google Maps? For example, the Queen's tomb?
Lady: Those are not accessible.
Me: So it's just the theatre?
Lady: Yes.
Me: Isn't it a bit exaggerated to call it an "archaeological park" when it's just the ruins of a theatre?
Lady: …. would you like to take the combined ticket?

So not more than the two museums? Basically yes, but both are pretty amazing. The Museum of the Royal Tombs has already been praised by previous reviewers, and I can only agree. The photo shows the golden Gorytos, a case for bow and arrows, one of many spectacular finds from the Royal Tombs. 
The central exhibit in the new Polycentric Museum of Aigai is the restored façade of the palace, or at least a part of it. Apart from a few sculptures, it is mainly jewellery and everyday items that are on display: lamps, arrowheads, small clay jugs. But they are nicely presented, some showcases looks more like an art installation. So even such ordinary objects as iron nails are a real eye-catcher. The DiscoverVeria website shows photos that give an impression of what I mean.
The Polycentric Museum was opened in December 2022, it is located in the buffer zone. But strictly speaking it is the "New Central Building". On the DiscoverVeria website (link above) you can read the following:
"A multifunctional and constantly evolving museum of a 146.000m2 size with various distinct units scattered around the area. It integrates and connects the new central building not only with the whole archaeological site of Aigai, namely the Palace and the tomb cluster of Temenids, but also with the world-famous Museum of the Royal Tombs."
So there is some hope that one day the entire archaeological site will be open to visitors. Certainly a reason to revisit, there is much more to see than what is currently accessible. And who knows what is still hidden beneath the ground.

And finally a recommendation: visit the Church of Saint Demetrios at Palatitsia. It is a little gem with wall paintings from the 16th century. The connection to the archaeological site is that it was built with material from the palace. It is located on the edge of the core zone and can be reached from the Royal Tombs in 30 minutes on foot or 5 minutes by car.