Ledger is problematic because its closed source so you can't verify and sign the code firmware updates. And a cold storage wallet should be airgapped, generated offline, and use partially signed transactions. Your seed can be generated with dice, so you don't have to trust that the device generates entropy.
If your wallet recieves firmware updates that can't be vetted and verified or it is connected to the internet, it should be considered a hot wallet.
If you use Ledger Live you have to rely on ledgers node and they have your xpub Unless you run your own node and a 3rd party wallet software. They have also leaked customer information that have put millions of people in the crosshairs of malicious attackers.
But sure continue use your statist ledger with good conscience.