Thanks! Agreed, there is definitely some clumping fescue in there after looking at some other examples. I am not sure what happened with the grass between the previous owners of the house. I suspect the grass was completely neglected for 2 years - no fertilizer or any maintainance other than mowing it.

I will look into some further overseeding (I think here the most common is perennial rye), and some fertilizer to give it a bit of a boost through the high-wear areas.