I've been in the US for more than 5 years on an F-1 visa, and I am a resident alien for tax purposes in 2020. I am currently a student at a US university, and I received some stipend earnings in 2020. Despite the fact that I am a US resident, I think the tax treaty between the US and Russia still applies to my stipend income -- Article 18 of the treaty contains time limits on the exemptions for trainees and researchers, but not for students. My university did not issue either W-2 or 1099-MICS, and, as far as I understand, they are not going to issue 1042-S either. I am not sure what to do in this case. IRS Publication 519, section 9 paragraph "Students, Apprentices, Trainees, Teachers, Professors, and Researchers Who Became Resident Aliens" states that "in most cases" I would not need to report tax exempt income, as long as it is not reported as taxable income on some form. It also seems that I don't have to submit form 8833, because I am a student. Is it really ok to just not report the stipend earnings in this case?
Yes, it is OK to not report the stipend earnings in this case.
As your university is not reporting your stipend as taxable income to you, you are not required to file a tax return to report it.
Your status as a student exempts you from having to file Form 8833 to state you are exempting your stipend from taxation under the US-Russia Tax Treaty.