I did this and didn’t mow my lawn. It works either way. I had just cut my lawn 2 days before but I also put down a growth regulator on it too. My yard is the darkest forest green lawn. I used 6 ounces of iron per 1000 though. Lawn is looking good.
So looking up Epson salt, it's basically Magnesium sulfate, which is also used as a fertilizer. So it seems like a AdBlue kinda thing, same ingredient but sold for a different purpose. I'm guessing it will green up from it, only if it has a magnesium deficiency, but I'm no expert. From what I understand, a plant/grass needs all sorts of things to get green, of which Nitrogen is a big one and easy to deplete. Thats why usually if you only put in N, it will green up as it was the limiting factor. But its possible there are other ingredients that are the limiting factor. Applying that one will cause greening up in your situation. Thats why different people swear by different sorts of products as they saw result in their situation. With liquid iron I have even heard its physically making the leaf look darker because of the chemical being on the leaf, reflecting differently in the sun.
I mostly use granular products and a schedule. It gets expensive to try different products but when you have the right combo make sure you stick with it. I use Milorganite®, Scotts weed and feed triple action, Ironite, fungus/grub control and Epsom salt. I mix them all together for the spreaders and apply 1st weekend of the month. I dethatch/verti cut then aerate in the spring before applying my first application. I use a spike aerator and not the core version as I want to just keep the soil from being hydrophobic and have a place for the granular products to be absorbed. I have a lawn plug tool and when the dogs give me burnt spots I use the tool and swap in a plug. No seeding required. Since I am the only person on my street with a cared for lawn it looks great, not quite like yours.
It's 300 square feet and the automatic sprinklers were installed by the builder before I purchased the house. It takes a bit more than 1 watering can of water. Thx for your comment