The company that developed Banjo-Kazooie, Rare, was indeed bought by Microsoft. Since then it has only appeared on Xbox consoles. I highly doubt that it will ever return to Nintendo consoles, as Microsoft doesn't want to create games for a rival's platform. I also doubt we'll actually see any new games in the series any time soon, as most people consider 3d platformers and outdated genre. The latest game in the series, Nuts and Bolts, was released in late 2008, was very different from the previous two games, and we haven't heard anything else about it since.
A similar style game recently released on Playstation, Xbox, PC, and is coming to switch. Yooka-Laylee is a very similarly style game created by Playtonic studios, which is comprised mainly of member of the original Rare team. It features similar art style, characters, gameplay, and those silly voices everyone either loves or hates. So if your interested in more Banjo-Kazooie type action, you should check it out if you haven't already.