Without knowing the exact install method used its hard to say how bad the problem is.
You can scrape it out but be careful not to nick the wires in the floor. Grouting will probably just crack again because you are getting movement. You could get a color matched caulk and put that on the crack and it might hold longer but who knows.
Anything you do will just be a temporary fix and it will happen again. Something is moving and will probably continue to move.
i wonder if SAKRETE Mortar Repair or Loctite polyurethane concrete PL S10 would be good?
I'd like to know if the mortar repair products would hold up in a grouted area?
No - I got it remodeled 15-20 years ago and that's when the tile went in.
Any ideas on types of caulk to use?
Not really a good option.
If you don't know the brand and color originally used you will have to guess. Home depot and lowes both sell color matched sanded caulk in the tile section. You can look at those and try to find one that is close. If you know the original color it might be easier to find a match but with how old it is you probably will have to just find something close.
Looks similar to mapei chamois, which has been popular for a long long time and I used it a ton 15-20 years ago, man that makes me feel old.
