Private key question

Hi all - question here from someone very interested in Ethereum and best security practices.

For someone that uses a hardware wallet, I've noticed that when you connect it through Metamask, you get hundreds of addresses that you could hypothetically use. You can also use your hardware wallet for other EVM chains, Bitcoin, etc.

Let's say 1 of my Ethereum addresses was subject to a smart contract issue, where I signed a message that allowed the hacker to drain my wallet. Would this also allow them to drain my wallet on Bitcoin, on my other EVM wallets, on my other Ethereum wallets -- presuming they were all generated by the same hardware wallet?

I know when you create the wallet you only have 1 private key (eg. 12-24 random words), but not sure how it exactly works technically on the blockchain level.

To this extent, how safe would the other wallets be if 1 of the wallets was compromised on-chain?