In sparrow and electrum wallet, the server will know all your public addresses that are inside your wallet.
Is it the same way with a hardware wallet? When I connect the hw wallet to a third party wallet, will the server know all the addresses that are inside my hw wallet?
If the third party wallet is an SPV wallet, it is the same. But if you connect it to your own node, you will not rely on central servers but your own node. You can run your own Electrum server and also there are ways you can use hardware wallet with full node.
But in theory there could be third party wallet that give you a choice to not query all addresses at the same time.
It depends on the gap limit.
I have also read 2 things that seem contradicting. There is a popular scam where they sell used hw wallets after they have copied the seed phrase so they can recover it later when the new owner puts money into it. That's why they officially warn to never buy second hand hw wallets. But I've also read you can create new seed phrase and private keys. You can have several wallets inside the he wallet and switch between them so third party wallets will not know about the other wallets you have on the hw wallet. If that's possible then the scam threat isn't that serious if you just create a new seed phrase?
The seed phrase or the private key are generated by the bad people, which means the wallet vulnerable. Also it can be in a way you will think you are generating it but you are not as it has been generated before and known to the bad people. The best is to just buy a reputed hardware wallet from a reputed source. Although, I prefer to use wallet like Electrum on a airgapped device.
A friend asked me if she can just create a new address in her hw wallet, will it be secret address? Or is it likely coinanalys or some bitcoin server would be able to link that new address to all the other ones inside the hw wallet?
Central servers do not just know only your addresses but also your IP addresses and that can help in knowing other wallets.