Don't think the previous explanation is quite right.

Yes, the money in your account (aka commercial bank money) is a debt that the bank owes you, payable in cash (central bank money). The banks need to borrow cash from the ECB to make good on their debts. Only the ECB is allowed to literally print cash.

Central bank money is, by law, what you can pay debts with. It's not backed by anything. It's what backs other things.

The banks create the commercial bank money simply by going into debt, but they are limited by the fact that they have to borrow cash to make good on that debt. The ECB raises the interest rates at which they lend out cash, if the banks create too much money and create inflation. It lowers the interest rates to encourage the banks to create more money for investments or consumer spending.

1 Problem: People use less and less cash. If people don't want cash anymore -> infinite money glitch. This is easily fixed without a central bank digital currency (CBDC).

2 Problem: Banking crises. What happens when a bank can't pay its debt? Until the early 20th century, that meant that your money was gone. In the wake of the crisis that triggered The Great Depression, this was fixed with mandatory deposit insurance and other legislation.

You still have the problem that our payment infrastructure - vital for the day-to-day economy - relies on banks being able to make good on their debts. In the US, retail and investment banks had to be separated by law (Glass–Steagall Act). This provision was repealed in 1999. This is often argued to have contributed to the problems around the 2007-2008 banking crisis.

If the ECB were to take over the payment infrastructure, it would be safe, no matter what happens to the banks. This may be not nearly enough to actually deal with banking screw-ups, though.