Subdivide by selection once (path to an adaptive subdivision modifier)

Our subdivision surface does feature multiple subdivisions. But it only could subdivide an object as a whole.

If you like to subdivide a part of the mesh, you can split the mesh by selection and apply the subdivision surface node to the selection part. Something like this:

However, the subdivided part would not merge well with the remaining part.

I suggest a subdivision surface node, which does a single subdivision step (Catmull Clark). It takes a selection. And it merges well subdivided parts with remaining parts.

To simplify the subdivision operator, this node only does a single subdivision step.

A motivation: In an iterative process, using refining selection by distance, this node could be used to describe an adaptive subdivision modifier