Does adding vinegar to rice while while boiling reduce stickyness or improve hardness?
No, it does not.
I was pretty sure from the theory of it that it won't help. Acid makes cell walls harder, so you can use it e.g. when you are cooking potatoes. But in rice kernels, you have basically no cell walls to harden, everything is starch granules. So I saw no reason why it would work.
Theory is nice, but not always enough for writing answers. There can always be an effect I don't know about - just because the mechanism I am thinking of doesn't apply here, it doesn't mean there isn't a different one. But it so happens that I recently bought a package of rice from a new brand, and I hate it. It always cooks up mushy. So today, I decided to give it a try. I simply used the rice cooking program of the instant pot with the usually-mushy jasmine rice, and added citric acid. The rice had an obvious sour taste to it, but it was as soft and mushy as ever. I didn't see any difference in texture. Even though it's a single data point, I still feel confident enough to write the answer - you will not get any more hardness, and you will confuse the eaters with sour rice.