I'm aware this is possible by doing manual animations, but is there a way to create a simple template that I can re-use for every podcast I edit? It'd be great to just do this on Premiere. I'd need to be able to transition back and forth between the two shots, and possible have inserts as well.
Study up on how to use the Essential Graphics panel in both programs to create custom templates. If you want this specific transition style it's gonna be tricky, though since there are several mattes involved that mutually mask stuff to create the illusion. Chances are that this may not satisfyingly work in Premiere, so you may need to set up a project in AE where you just replace the relevant footage bits every time.