Train Prague to Munich with stopover

Apart from Regensburg (only about 100 km from Munich), there isn't much on the Bavarian side, because the no-man's-land of the Upper Palatinate Forest begins northeast of there. But on the Czech side, if you take a small detour, there's Cheb, Karlovy Vary, and Mariánské Lázně. Along the direct route are Klatovy and, of course, Plzeň.

You could take a little side trip to Nuremburg. Plenty of history and great architecture.

Furth im Wald is the first stop after you cross into Germany. It has a big Dragon fest in the summer. I can't speak for winter.
Domazlice, the last stop in Czechia, is listed as a "picturesque" town in my old German Road Atlas.
https://www.visitczechia.com/en-us/things-to-do/places/landmarks/cities/t-domazlice

Is there a quaint storybook type village in Germany that might be worth stopping to explore
on the way for one of the days? Are any with the mountains in the background?

Eh. No.

The mountains you want to see are well south of Munich, in the southern-most part of you Bavaria. You won't see them without going south past Munich. And the architecture you envision, probably Fachwerk, is not the architecture of the Alpine regions.

Furth im Wald is the first stop after you cross into Germany. It has a big Dragon fest in the summer. I can't speak for winter.

That reminds me of a local saying: “Aus Furth will jeder furt" (furt = fort)”, approx. “Out of Furth they all go forth”.