I don't know if you deliberately fuse the hardware wallet part with the necessarily online software wallet part (which as I already wrote is usually watch-only).

With closed-source firmware we don't and can't know what the firmware does and what functionality it provides. As I'm not particularly interested in the Ledger crap, I don't know if and how open-source Ledger Live is. My only perception is that this is crappy software with occasional sync issues and it tracks the shit of its users. Due to Ledger Recovery service subscription, we know Ledger Live contains code that can interact with Ledger hardware capable of this Recovery subscription to exfiltrate encrypted wallet seed shards and transmit them via the internet. No question, I consider this very bad.

Even an air-gapped hardware wallet needs an online software wallet part to transact and broadcast a transaction. Is such an air-gapped hardware wallet by your logic not offline?

Anyway, closed-source Ledger crap is evil and something to avoid based on what this company and its executive morons try to sell as their hottest shit.

I have no issue when a USB connected hardware wallet is not "offline" for you. For me it's offline when I can verify that the firmware code doesn't contain any code for networking and USB related code can't access or transmit main wallet secrets. Same goes for the software wallet part that talks to the hardware wallet. If there's no code to connect wallet secrets with the internet, I consider this as some sort of barrier like an air-gap. No important secrets can be exfiltrated from the hardware wallet. Offline enough for me.