The publication is an article in a local newspaper, not from a numismatic magazine. The article was about the collection "Van Woelderen" in the Urban Museum, and in that article specifically about historical medals.
"BAV" is the abbreviation for "BAVARIA", but no idea yet about "BYR".
The name of the kings are not mentioned in that article but I've found another website about this medal and you're right about the kings:
- Elector of Saxony: Friedrich August II (Frederic II)
- Elector of Bavaria: Karl Albrecht (Charles Albert)
- King of Poland: August III
On this website the abbreviations are also explained, except for "BYR". That's a pity because I knew the others but I don't know "BYR". I also didn't know "Oostene" stands for "Austria".
Just like on the article in that old newspaper, you also can see here the obverse is the side with the kings, and the reverse is the side with Maria Theresia and her son.
https://www.cngcoins.com/Coin.aspx?CoinID=221516