Here’s the problem now. You really don’t have a whole lot of choices due to the existing paint will keep from any floor finish adhesive or thinset from adhering to the existing substrate. Also grinding the concrete will make a lot of dust in the building plus clean up if done wet.

First I would try a heavy duty buffing machine with a good course pad and a stripper product that will cut that carpet glue residue. Once you get that off It will be more cost effective to go back with a concrete paint to cover up the existing.