A hardware wallet that connects to an internet connected device directly is itself connected to the internet.
Not at all, in my opinion. What you say implies that basically every hardware wallet would be connected to the internet, which is wrong.
For wallets with open-source firmware, we could check this. For wallets with closed-source firmware we can't. Nothing new on this front.
I guess that is fair. I mean for most devices the firmware is not open source so we can't be sure of things in general. In the case of Ledger we don't know at all. Now my question is are most hardware wallets fully open source or are most fully closed source or only partially open?
Second an offline wallet is one that is always offline, otherwise the word offline wallet is meaningless..
A cold wallet is by definition offline and has to stay offline for all time, otherwise it's not a cold wallet anymore. The moment a cold wallet becomes online, it looses its "cold" status forever by definition. Being online, the wallet becomes hot and can't get "cold" anymore.
You understand me! On this point we agree completely. I tried to make this point but the users got it all wrong. It has to be offline all the time since creation.
We must be careful with the logic that we use, otherwise we could consider mobile wallets as offline wallets as long as we keep them then disconnected from the internet. Lol
Thats literally the definition of the word "offline". In technical contexts, it means disconnected from the network, in this case the Internet. So yes, if you have a wallet installed on a device that is disconnected from the network, that is by definition an "offline wallet." Im not arguing here that this always makes it a good option for cold storage. It depends on the setup.