Yeah but the banking products are provided by a wholly owned subsidiary (savings accounts and loans) and a partner company (checking accounts and debit cards), both of which are banks. The products are indeed offered by banks owned or partnered with Square, but not directly by Square, Inc. itself.
Regardless, if Square were to offer legitimate 2FA I would probably feel more comfortable using their debit card for daily life..Can't seem to find any details regarding this on the FAQ though.