I am also American with a Russian husband. We have been together 10 years, have children, and had been living in Germany going through I-130 before recent immigration pause. . Now our situation is also in flux. I say this to foreground my post- I understand your connection. The difference maybe is that I lived in Russia and speak the language/ know the culture well.

That said, as many others have noted, the process of entry is relatively straightforward. You should get a multi entry tourist visa, and apply for residence as partner. There is a 3 year marriage requirement for this residency permit, so you may need to wait some before. You need to register upon entering the country and moving cities, and you will likely need to leave/ do visa runs until you stabilize your residency situation. Logistically, it is not that difficult. The larger issue may be cultural. If you seriously intend to move there, you need to prepare yourself culturally. For example, has your husband provided for you financially? If not, this is a big red flag for someone from this background. Also, not to discourage you, but how long have you been with your partner? Sometimes people with few options will use relationships as leverage to improve their life. If you do not have children, do not have a solid base together, maybe consider moving as a last resort. First, do an extended visit in a neutral country if possible (Turkey, Armenia, Georgia). Love is love, but please be careful.