Just an update for anyone interested - Everything went well for us and my fiance is now my husband
The medical interview in Jerusalem went smoothly. He really didn't have any health records to bring except some hand written vaccine records and documents from his childhood in the USSR. Fortunately Do Jonty was able to read Russian and was able to determine the vaccines needed. My fiance printed out an official "recovered from covid" form from Gosuslugi and when he showed it, the doctor said there was no need for the covid vaccine then. He actually crossed it off the form and marked him as having completed the vaccine requirements.
On thing about the medical exam though... They say your exam results should be ready within a few days, but this was not true for us. The bureaucrat who does the paperwork for the embassy was way behind on his work. My fiance went there after several days and was told that they might get it done the day before the interview. We had two weeks between the exam and the visa appointment, and two days before it, my fiance went to the med center and sat outside the bureaucrat's until they were about to close. He literally had to negotiate with the guy - he just couldn't be bothered with it - and remind him of the disaster it would be if it wasn't done in time. He did complete it at the end of the day. What's crazy is that if you're getting a CR1 visa, it's digitally submitted, so there's know way to know if the guy did it in time. At least with K1 you have to get a physical packet from him.
The interview at the embassy went very well. There were two parts. The first woman took his documents and asked some formal questions. She spoke russian and was a little cold at first but actually warmed up a bit went they talked. She didn't really spend much time looking at the documents. For any russians reading this, you will definitely need your военный билет even if you didn't serve in the military. It still says you didn't serve and they do want to see the original. After that, he moved to a different window with an American officer. He was actually quite friendly. He asked some basic questions about how we met and very basic things a couple should know. Nothing at all to worry about here. After about 15 minutes he said that he can come back and pick up his passport with the visa in a few days. And that was it. As for getting the passport back, they had him come back several days later and he went to a window outside the embassy and picked up his packet. Online there had only been an option to pick it up from the post office, but they never even mentioned that at the interview and just gave him instructions to pick it up there.
We immediately changed our El Al flight to the nearest date and got him out of there within two weeks. Entering the US was easy. They pulled him into a special room at the NY airport and some questions, took his packet and sent him on his way. We're married now and sent in our application for adjustment of status. He just received his work permit and social security number, only a month after submitting the application.
Good luck to everyone else going through this!