If a company wants to hire you but asks you to switch banks because the bank you use isn't familiar to them. Would you find this suspicious?

I don’t know. When I had my first job at 14 at Burger King they made me open an account at a bank of their choice where they deposited the money. It was the only bank they used

You definitely do not have to switch banks. Keep your account(s) at the bank that you are currently with and just open a second account at the bank they want you to open at