Yakuta, my husband does all the deep frying, but sometimes I slice onions very thinly as you described, then toss them in seasoned flour before frying them up in a regular skillet. (usually after frying something else.)
They are a light and crispy addition to steak, burgers, fried fish, whatever.
These are a different thing from the regular breaded, deep-fried onions rings.
For gravy, I like caramelized strips of onions. I want them cooked soft, but I like to see the pieces.
Still, an onion paste could be useful. Sure would be good to use in a salad dressing...combined with olive oil, assorted herbs, butter and used over pasta ...as a spread for bread...as a seasoning for vegetables...added to sour cream for dip...there are all sorts of possibilities.
We get by with a little help from our friends