It is wrong to call hardware wallets "offline wallets"
First of all, how about this pinned post that I quoted this below content:
Cold Storage
Cold storage is achieved when Bitcoin private keys are created and stored offline. Private keys stored offline are more secure since there is no risk that a hacker or malware could steal your coins.
There are three ways to create cold storage: paper wallets, hardware wallets, and software wallets run on offline computers. Think of cold storage as your savings account. Use it to securely store bitcoins that you don’t plan to spend.
Offline wallets are also called cold wallets because their seed phrase and keys are not generated online and not revealed online which makes it more safe and secure to online wallets. There are many clipboard malware we have heard of before that stole coins while the recipient address was changed to a hacker's address while sending on a hardware wallet. Also we have heard of some other vulnerabilities before, but yet never heard of a malware that reveal the seed phrase or keys of a reputed hardware wallet. But if there is any, you can point it out which will make me to be wrong about this.
Also hardwares are getting modified, it is now very possible some hardware wallet can generate keys and addresses without even connecting it to a device like computer or phone. But the fact still remain that the seed phrase and the keys on hardware wallets are generated offline, stay offline if not imported on online wallet. The reason they are called cold wallets, cold wallets are offline wallets.