Cultural solution first. Water deeply and infrequently based on the grass. When it looks thirsty (won't spring back after stepping on it or looks dry) then water at least an inch. Put a small can (tuna cans are ideal, but anything will do) in the area of the sprinkler so you know how much your putting down. Cut high with a sharp blade. Fertilize. It may be too hot for chemical fertilizer. If you don't have an aversion to Milorganite it would be ideal. Apply at the rate on the bag. Some may offer that fertilizing is wrong, but from your description the grass is weak and it needs food. Feed the grass and kill the weeds is how I see it. Fixing the weeds. Before you apply the Menards product read the label to see if it is effective on crabgrass. If not, then your local big box should have a product that would work. Bayer and Ortho are pretty good products. Hose end sprayer seems to work well. Same stuff should be available in granular if you prefer spreading, but liquid seems to work faster. Just follow the directions. Towards the end of August or first half of September you should plan on overseeding (cut grass short gradually, core aerate, apply new seed and fertilize). There are several threads with some great instructions on renovation. Patience. It will take some time to heal. Renovation this fall will be your best time to improve the lawn.

Start with a good, reliable soil test. Contact your local OSU Cooperative Extension Service office for assistance about this. They will send your samples to either Penn State or the University of Kentucky since the soil testing lab at the university has been closed, but the results you get will be good. This soil test will tell you about your soils pH (for a lawn that should be in the 6.0 to 7.0 range) and the levels of Phosphorus, Potash, Calcium, and Magnesium. Then you can dig in with these simple soil tests, 1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top. 2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains� too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up. 3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart. 4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell. 5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy. to see what else your soil might need to become a good healthy soil that will grow strong and healthy plants. Once you know what the soil you have is now then you can begin to plant what you will need to do.

I agree with this suggestion. It is not helpful at all that you can only see United States as the person's location. Which is why I have mine showing 7b NC. I used to frequent the building a home forum a lot and another thing we needed to know there was what kind of climate the person had for answering questions about building envelopes and energy useage, etc. That is why mine also shows Mixed-Humid, which means we get very hot as well as cold and we are in a high humidity area. One of the most challenging building climates. https://www.eecbg.energy.gov/buildings/residential/climate_zones.html

That is a very well thought out plan. Good for you. That plan should keep new weeds from starting, but you still have the old ones to dig out. Killing grassy weeds in grass is hard to do. You can spot spray with something like Grass b Gon, but the overspray will kill the surrounding bermuda. If you can shield the surrounding grass with cardboard or something you could spray the grassy weeds out. I'm really interested in the EGO equipment you bought. I've gone all electric, but a few of my pieces are corded. I'm interested in the mower and string trimmer. Im relatively happy with my Black and Decker battery mower and trimmer, but I could be happier with the trimmer. Please let us know if you're happy with the EGO brand. More important than the mowing (low) and fertilizing is watering. Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.