privacy – Are transactions from two separate bitcoin accounts on Ledger Nano S independent of each other?

There are no accounts in Bitcoin. Its based on UTXO.

According to support.ledger.com:

When you add an account, Ledger Live gets its unique extended public key from your Ledger device. Thanks to the xpub, Ledger Live then generates individual public addresses and checks their balances in the blockchain to calculate your account balance.

So accounts in Ledger Nano S are HD wallets with a master public key and lots of addresses.

If there are no transactions there will be nothing on blockchain to link them. Ledger servers have the information about your XPUB, addresses etc. so you should use your Bitcoin full node for better privacy

In some cases there can be other ways to link two transactions, addresses etc.

  1. Some information shared online by user.
  2. Coinbase in this example has all the information about user and one of the wallet. If user is not using his full node and explorer, IP address can be used to link.
  3. Forced address reuse: https://en.bitcoin.it/wiki/Privacy. Sending small amounts of bitcoin to same address and wait for user to spend them hoping to get more information about wallet.
  4. Anything else common in those two transactions: time, amount, type, version, locktime, fees, change etc. Most of them should be different in this example.
  5. Future transactions from these two wallets.