These association logos are commonly used for the serbian third divisions and are official logos. Here the Srpska Liga Beograd website (serbian 3th tier Belgrade region)
https://www.fsb.org.rs/takmicenje/srpska-liga-beograd/
I'm agree with you about Zonske Lige (4th tier) logos that are more specific
That's the website of LND Abruzzo region in Italy
https://abruzzo.lnd.it/
The logo you see on the site is used for all three regional divisions in the fifth, sixth and seventh division because they are all managed by LND Abruzzo but are three different divisions. The same goes for LND Lazio, LND Campania, etc.
LND means national amateur league. It works like serbian regional leagues logos