The two most important elements to the security of your coins is the seed you generate when you first fire-up your hardware wallet and the private keys derived from that seed, which sign transactions allowing you to spend your coins. In the case of Ledger, the seed is only visible on the screen of your hardware wallet. It's native software, Ledger Live, never sees the seed.

The private keys are kept in a sealed environment known as the Secure Element. The keys only get used when you need to sign transactions to spend coins. For that, you need to physically allow your device to sign the transaction by pressing the two buttons on top of it. No software or third-party can see your keys or broadcast the transaction for you.

You can test that yourself if you have a Ledger hardware wallet.
If you use Electrum, create a new wallet for testing purposes. Run the software, click on Wallet > Private Keys > Export. Enter your password and Electrum will display the private keys of 20 receiving and 10 change addresses by default.

Try the same with your Ledger. Plug in your Ledger and connect it to Electrum. Open your bitcoin wallet and try to view and export your private keys. You will see that it doesn't work because Electrum can't access them.