Am I really understanding how the "Trezor Model T", and hardware wallets in general, work?
Hardware wallets such as the Trezor ones you mentioned are only a secure method of storing and using your private keys.  When you want to send BTC, that transaction will be signed mathematically completely within the confines of the key itself.
One could design a hardware wallet with a full user interface, negating the need for a separate computer all together, but that would be far more expensive; in the realm of the price of a modern mobile phone.  Keeping the code inside a Trezor to the utter minimum reduces the potential for security weaknesses and improves reliability, too.