Elkay is a manufacturer of inexpensive sinks. Franke (like Scanvik) is an expensive manufacturer.

The 14-15" depth (front to back) and the self-trimming double sink which is about 25" wide is the challenge in a bar sink.

Since you don't have a disposal, some the "noise" issue that people have concerns with aren't as great. The the guage of the metal can be an issue if you try to (for example) break-up some frozen cubes of ice ;^))).

The bar sinks in the somewhat larger sizes often come in single underhung sizes, rather than drop-in and self triming units.

I think the challenge is going to finding a small one that works. I would suggest that you NOT get something shallower than 8". Aside from cleaning issues of soaking the plates and dishes, the sink will get pretty wet if you're under way and using the sink whilst healing. (I love to use that word 'whilst' :^)) )