The router plane is one of those tools that used to be really common, but with the advent of power tools vanished into obscurity. I was with a woodworking group recently watching a lecture on using a router table and the lecturer held up a book to show a picture of an old Stanley #71 to show what routers used to be like. Most of the 40 odd people there didn’t know they existed.
The other thing is, they are nothing like the power tool called a router. Router comes from “to root” which means something that burrows under the surface. That’s exactly what this tool does. It doesn’t spin, it doesn’t make fancy profiled edges. It goes below the surface of a workpiece and planes it flat.
Use this tool to clean up the bottom of a mortice, or to make sure tenon checks are perfectly flat, or use it to tidy up after you cut a dado to make sure the mating piece fits perfectly.