Reopening this because a lot of users have been facing the same issue.
It turns out that there are two different BUSD tokens on Polygon:
Binance-Peg BUSD is what Binance (the exchange) uses for BUSD transfers. Corollary: if you’re sending BUSD to Binance, I suggest you use the same.
I have pushed an update to the tokens list that now shows both the tokens with clearer names. If you have a balance on either of these tokens, it should now get auto-discovered on your portfolio.
You may need to restart your browser for the tokens list to be refreshed.