I have never seen a purposeful gap between the slab and the foundation stem wall in a basement. The only two scenarios where it would be useful are: 1.) if an insulation thermal break was installed, but that is only a recent detail so would only show in newer construction; 2.) an interior french drain system, which most likely is retrofitted and allows water coming through concrete block walls to drain in the gap. Do you have either of these?

Yes. The entire perimeter has a space filled with expansion gap fiber. In some cases the entire gap is visible and you can see the fiber (the big gaps). In other cases they were a little more sloppy and the concrete appears to have been pushed over some or all of the fiber (smaller gaps).

The house was built in 2004.

If they used the asphaltic fiber expansion joint, then I would probably seal it with urethane first, which would help with radon management anyway. Then since you need a gluable base, I would just stick with standard rubber wall cove base (e.g. Roppe at HD) which I believe the toe kicks out 5/8".

Great minds think alike - I already have multiple tubes of sealant for just that.

5/8" may cover most of the gap, but some is wider yet. Have you seen any with a toe closer to 3/4"?

Probably, but it might not be obtainable at the big box.