Most of the "tokenized Bitcoin" you're referring to is just an ERC20 promise of redemption from Bitgo's coffers. It's not at all comparable to Bitcoin's Lightning Network.
All I know is there's 148K Bitcoin locked in tokens, which is nearly 1% of all Bitcoin and that people are finding more utility in tokenizing it and providing it for liquidity and yield on various DeFi platforms than on Lightning network. Maybe that will change in the future, but right now, that's the case.
More tokenized Bitcoin is transacted on the Ethereum network every day than on the Lightning network, by orders of magnitude.