If there will be a Bitcoin 2.0 or a change of network from POW to POS then not only the network congestion is being fixed but many more, and also it can reduced the energy consumption.
I do not think that there is a relation between converting to POS to the network congestion unless people leave BTC after it converts to POS. The thing with POS is that, the security of the network is not as strong as POW. Check this article[1] [2]for comparison. The network congestion solution relies on the blocksize limit and the frequency of creating blocks. That should be modified IMO if one wanted to solve the congestion of network.
[1]
https://cointelegraph.com/learn/proof-of-stake-vs-proof-of-work:-differences-explained[2]
https://river.com/learn/proof-of-work-pow-vs-pos-proof-of-stake/