Looking for a yard/woods grass that fits these criteria:

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Couldn’t hurt to scatter a bag or two of wildflower seeds out there. You can usually get some big bags of a Wildflower Mix at HD, this time of year.

As Scott says, you might get some pretty flowers among the stuff that come up naturally.
If you can’t mow, wildflowers are your best bet to improve what will happen naturally, and you might help feed the pollinators.