It appears that in the new map viewer, the functionality to select a record from the attribute table of a feature service, and then zoom to it, has been removed.
Is this correct?
If so, what is new procedure, in the new map viewer, for selecting a record from the attribute table and then zooming to it?
That appears to be correct. The procedure you describe is a part of the Table widget recently added to Experience Builder, so it's certainly possible in the 4.x JS API.
For the time being, the map viewer itself lacks this function. Perhaps that will change with the next update or two. I would certainly upvote an idea like this if you posted it in the Ideas space. For basic configuring and editing, it's often nice to just use the map viewer rather than build a fully-fledged app, so it would be good to see this functionality in the new viewer as well.