Reddit reviews American Standard M906667-0070A Mounting Ring for Pekoe Kitchen Faucets, N/A
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Those are jamb screws. They actually don't tighten into anything. No wonder it broke off.
Look at this picture:
https://www.amazon.com/American-Standard-M906667-0070A-Mounting-Kitchen/dp/B004FVA3ZM
A little different than yours, but you get the idea. Unscrew the intact one until it turns easily, and see if you can get some needle nose vise grips on the broken one:
https://www.amazon.com/Needle-Locking-Grips-Clamp-Pliers/dp/B06Y3NRNQY
If you are lucky, you can that one to loosen as well. Then you tighten the big nut that is hidden under all that silicon sealant. You use a basin wrench for that:
https://www.homedepot.com/p/3-8-in-x-1-1-4-in-Telescopic-Basin-Wrench-70225/203550188?MERCH=REC-_-PIPHorizontal2_rr-_-204277452-_-203550188-_-N
NOTE: for illustration only. They have much cheaper ones....
Then tighten the jamb bolts. Just enough so the big nut cannot back off. 5 foot pounds, maybe.