Indeed there has been no official news issued by BSC regarding the increase in gas prices, and probably will not happen in the near future, BSC was developed based on a small concept,
The increase of the fees will depend on the crowds of the transactions in the blockchain moreover if the crowd enough, commonly there will be little bit increasing.
But BSC increase is still very tolerance and seems not still no problem for us, moreover even if we are transferring big amount of BSC tokens.
However if the ERC20, we have see how many increase that can happen on in seconds, the difference can be more than 20-hundreds Gwei. This is bad and why I really hate using Ethereum blockchain. But we cannot still avoid because most tokens stull use ERC20 blockchain.
It's just a matter of choice, if many projects use the ethereum network, then we also can't do anything, but today many projects have switched to the BSC network, this is more interesting when compared to 5 years ago, using the ethereum network makes us a lot the costs required, especially if the coins or tokens we have are only a few, then the gas costs are much greater than the exchange of results we get.