Do we know if Budapest is actually serving as Budapest in Homeland or is it just a cheap place to film that could serve as Russia (which is what they did for Red Sparrow)?

All we know from Dante is that Simone and Wellington met in Budapest. So Budapest could in fact be Budapest. But we don’t know for sure. I’d like to believe, as Gail referred in one of the recent podcasts to John le Carré’s Tinker Tailor Solider Spy, that “… the purpose of the mission to Hungary was to get the name of the mole.”