The A1 bus (Trg Slavija → Airport) supposedly stops here when going to the Airport. The current OSM relation does not go anywhere near the Novi Belgrade train station, which seems to be an error. See relation/7025148 and https://bgprevoz.rs/linije/red-voznje/smer-a/90005, which have multiple differences)
A person working at the ticket office confirmed to me that the A1 does indeed stop near the train station, and I also have confirmation from a person having using the bus there in the past.

I do not know whether the information published by the Sekretarijat za javni prevoz online is generally reliable. I also don't know whether it is available in a licence compatible with OSM.

I asked the A1 bus driver stopping at Železnička stanica Novi Beograd (coming *from* the airport) where to find the bus going *to* the airport. There was a bit of a language barrier but he sent me down Antifašističke borbe and hinted that I'd have to go right at the intersection. I ended up taking the bus 600 so I couldn't survey where the A1 actually stops, but at least the bus driver's direction don't contradict the online information.

I did notice that the stops and most of the route of the other direction (Airport → Trg Slavija) in OSM seem to align with what's available online (see relation/7025041 and https://bgprevoz.rs/linije/red-voznje/smer-b/90005).