There is not a single good reason why battery should be added in Trezor Safe 3, but it's easy to connect it with simple power bank if you are paranoid.
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So, is the Trezor 3 able to be used by connecting it to a power bank? Or is it obligatory to use a smarthphone and a connect to the web page of Trezor?
I have always felt interested on using a hardware wallet by Trezor in a completely airgapped environment, but I have not had the opportunity to do so.
You can connect Trezor to a power bank. Still, you will not be able to use it to make transactions because Trezor does not provide features such as Bluetooth or other similar connections that can connect to other devices, such as smartphones.
I have a Trezor T, and it has a slot to place a Micro SD, but so far, its only function is to encrypt the PIN (https://trezor.io/learn/a/encrypt-pin-with-microsd-card)*, unlike the Cold Card, which has many functions related to using the Micro SD in the hardware wallet (https://coldcard.com/docs/microsd/).
* Even though the device is connected to a power bank, the PSBT feature on the Trezor T SD Card doesn't yet exist, even on the Trezor Safe 3; as far as I know, there is no slot for micro SD.