Not at all true, they’re lending the money in the bank. If you withdraw the money the bank can’t loan it anymore it’s the same money, just in different hands. It creates more circulation of the money through the economy but there isn’t more money created with magic.
The bank loans your money and pays you a portion of the return in the form of a savings interest rate. In essence the bank is just the middle man loaning your money to someone else. There’s no creation of new money. It just puts money that would be sitting idle to work.
There’s so much misconception about all this due to people looking to criticize the government/fed oversimplying complex policies to sound bites. Putting more money into circulation in the economy doesn’t mean money is created. It just means more is being used. There’s many policies that effectively create money, like quantitative easing/bond purchasing.