I purchased the PHB/XG/TG books and in character creation several of the options for backgrounds are not there. I know Archaelogist is supposed to be available. Is something wrong, the books show up with everything else?

The Archeologist (and Anthropologist) is not in the PHB, it’s from Tomb of Annihilation. If you purchased the PHB, Xanathar’s Guide and Tasha’s Cauldron, then these are the backgrounds you should be able to access in the builder: (https://www.dndbeyond.com/backgrounds?filter-name=&filter-source=2&filter-source=67&filter-source=27). if any of those are not accessible then click the following link and ensure your Account Entitlements are in sync: (https://www.dndbeyond.com/account/marketplace).