Is Cat 5e ethernet wiring still current? Do I need to rewire the house?

You can buy a more up to date cable to test it, see if it makes a difference, just run it directly for the test, across the floor, down the stairs under the door type of run. I doubt you will notice any difference but it will be much cheaper/faster then running ‘correctly’ for no gain.

No, I don’t think so. At least, not today. But that’s the thing, isn’t it? How many years should I plan ahead for?

No more than 20.

But other than that?

A rough number for bandwidth for 4k video is ~32Mbps. (just as a reverence)

If you are not editing raw video* (which involves manipulating large files) on multiple machines with a NAS to share the files: you will most likely never notice anything.

*Or working on CAD drawing from multiple workstations, or doing something other very specific that will benefit from very fast file sharing. When that becomes an issue you could always replace a particular run of cable. You and me will be long gone when 1 Gbps is no longer fast enough for general connectivity (if ever)

Worry about latency; optimizing DNS – bandwidth is no longer an important metric (when you get to ~1Gbps)