A hardware wallet generates the seed phrase with a certain standard.
Because of that, you can recover your funds with a new hardware wallet or with any wallet that supports a standard such as BIP39. You don’t have to be connected to the internet. Its just a little program that will always give you the same keys if you input the same seed phrase.
To check your balance without the hardware wallet, you can simply use any wallet and connect the hardware device once. The wallet you use will now know which public addresses the hardware wallet has access to. This way the wallet can keep track of the funds without the actual hardware wallet.
If you wish to use a hot wallet, you would want to make a new wallet. DO NOT import the hardware seed into the hot wallet. This would make the hardware wallet pointless. Having a couple of % into a hot wallet may not seem as a bad idea if you send cryptocurrencies from time to time. A hot wallet will encrypt the private key when it is not in use, but will have to decrypt it in order to sign a transaction.
Hope this makes much more sense now. If you have furthure questions, feel free to message me back.