The bitcoin protocol doesn't have a concept of a "balance". Bitcoin uses "UTXO"s. A wallet will show a sum of all unspent UTXOs for all bitcoin addresses for that wallet as the "balance", but underneath, it's all UTXOs.

So an offline computer or device can't know what UTXOs it can spend without seeing the blocks and the mempool. So what works instead is having two devices. On is a connected device that prepares a transaction to spend and then a second, offline device, to sign that transaction. Thus, to do this the "partially signed bitcoin transaction" (PSBT) was created.

So that way you can have something like an Electrum wallet app offline (airgapped), and then another Electrum wallet online, which is the "watch only wallet" without the keys. The watch only wallet creates the transaction needing to be signed, and that transaction is transferred to the airgapped Electrum (e.g., via thumb drive) for signing, and then the signed transaction is brought back to the watch-only wallet and broadcast from there.

Now there are also signing devices that are also offline and airgapped. A poorer term for them would be a "hardware wallet", but they are not actually wallets, they are signing devices.

Here's an article describing airgap security, which might help you with further information.

Does airgap make Bitcoin hardware wallets more secure? https://shiftcrypto.ch/blog/does-airgap-make-bitcoin-hardware-wallets-more-secure