So far its the lightning that is working well for BTC and makes it better because of low fees.
UX needs work in my opinion. But you can use BlueWallet with hosted Lightning channels.
Lets say sharding is successfully deployed in ethereum and has improved their TPS, would it be possible for it to be with BTC as well without it being complex as creating channel like the LN?
I believe no. Ethereum is selling an idea, sharding, that's supposed to scale the network, but does the opposite. It's centralizing.