Not big thing, Web 3 based on blockchain technology focused in transparency of data and bitcoin is digital currency combines with web 3 provides more control to people without dependency on third parties . That's it.
I think you mention similarities but they have no connection at all. Bitcoin is not connected to web3 since it has an independent blockchain that doesn’t have 3rd party involved or dapps. Web3 is more focused on Ethereum based blockchains which dapps is building there project for there respective ecosystem.
Bitcoin has no connection to web3 besides the similarity of using the same blockchain technology.