Technically yes it is under the Banking Laws or Financial Services Act or whatever it is, they are registered as a bank.
No, technicalIy or otherwise, Wise is not a bank. If Wise was a bank, it wouldn't have to "safeguard" it's customers' money by depositing those funds with banks. From their website....
https://wise.com/help/articles/2949821/is-it-safe-to-keep-money-in-my-wise-account
"Wise isn’t a bank. We’re an e-money institution.
We’re required to keep your money safe and protected, and we do this differently to conventional banks. Unlike banks, we do not lend out customer money. Instead of protecting your money in a financial protection scheme (like FSCS), we safeguard your money".