What to fill the cut in quartz counter top with?
This looks to be a bad install.   The gap seem too large and that is with the epoxy filling it.  When a good installer deals with seams there is a process where they will clamp each side (suction cups or other methods) to push the pieces together.  They will add the epoxy in before sandwiching and then scrape off and level the pieces.  For different types of countertops they might leave this like this for a day.  

I see a wide epoxy seam, which means they did use epoxy but they didn't jam the pieces together.  So what happened is epoxy was put in (all the way through I am not sure about), then they fit the two pieces, pushed them together, then the epoxy pushed them apart... very little but enough for it to crack later.

The next issue is that these pieces should have been secured under the slabs to the cabinets in multiple places as close to the seam as possible and as close to the seam as possible.  I don't buy that this is normal, because I have seen it done right and have moved two pieces that were seamed together in my house to install new lower cabinets (the seam never broke).

What should you do now?  Call the installers.  If this isn't an option you need to buy a knife grade epoxy kit.  You can match your color or go clear.  If you have trouble finding these please let me know and I can look online.  (Probably won't be at big boxes)  Also if you are just going to lay some epoxy on here it can look nice but probably won't be permanent but is literally a 10 minute job.