It’s definitely The Doc. From showrunner Noga Landau:

“I don’t know if Bob knows this, but the Doctor, like, raised me. So I was worried… that I would come on [the video call to pitch his return] and scare him away. But then I realized that nothing scares Bob Picardo! I sent him the script and told him a little bit about the part he would have in the show for the first season. He’s going to do things we’ve never seen The Doctor do before — and The Doctor’s done a lot, think about it! — and he said ‘yes.’ I don’t think we had to twist his arm too hard, actually.”

As for the early 25th Century, there’s another show in development with Tawny Newsome concerning a resort planet. More of a workplace comedy and less exploration, though.