Privacy sidechain? Liquid network might be what you're looking for since they implement Confidental Transaction. For something easier or lighter on Bitcoin on-chain, MimbleWimble or other form of non-interactive CoinJoin probably are better option than CT.
Litecoin, which
signaled MWEB into activation in May 2022, has always been something of a test environment for features later implemented in Bitcoin. Litecoin was the 1st to have SegWit, a Lightning Network, and now MWEB, which is an optional privacy enhancing feature, used by Grin as default.
Here's a pretty in-depth
article about how it all works. I honestly don't see why this can't also be integrated with BTC, if miners signaled for it... maybe there's a good reason but I don't know what it is.
The reason could be the strong crackdown the US government has on privacy oriented softwares. Bitcoin developers seem cautious of new forks or changes in the network regarding privacy. Read through your shared link, and it's true of the privacy features on Litecoin network. The similarity it has with bitcoin's POW shows how simple it'll be to run similar updates on Bitcoin. But, Litecoin is not as mainstream as Bitcoin, despite its lesser fee features and faster integration of blocks, the government would be very strict on such changes if it came from Bitcoin developers.
A privacy oriented startup
Zksnack has removed their coinjoin features from wallets that utilizes it, such as btcpay, because they want to obey the government. Since they want to keep track of all transactions happening in the Bitcoin network launching a privacy oriented upgrade on bitcoin may get an immediate attention of the government on Bitcoin. Snowden on the other hand, has been reminding Bitcoin developers of this for a long time. He commends projects like Zcash for their privacy features, so I think of him as someone who cherish privacy on cryptocurrency transactions. But, he's been ghosted all through these years by Bitcoin developers. Hence the government happens to be a reason why.