Some of it may green up, it's still early. But those areas of dirt won't grow anything. Your soil looks extremely compact and that makes it difficult for grass to grow deep roots.

Mowing high and leaving the clippings is a good choice. Water deeply 1 inch per week or supplement to 1 inch if you have gotten additional free water in the form of rain. You can use a tuna can to measure.

Your going to need to improve your soil before you can grow quality grass, and it will take a while to get there. Here is what I would do (in this order):
1. Get soil test done (not DIY) but to your local extension office.
2. Rent a core aerator at big box store or hire a pro to do it. Not those spike shoes (core aeration, very different).
3. Apply either premixed wetting agent or research the baby shampoo trick. This helps remove the oil on the surface soil that typically repels water absorption and leads to compaction.
4. Apply compost tea and compost topdressing
5. Apply organic fertilizers (grains, soil bean meal, or premixed like ringer by Safer Brands)

Then next fall, over seed again and by next spring you should be in much better shape....won't happen overnight though

Thanks for the help. Now that I think of it, it could be compacted because that is where my wife always gets out of her car.