Banks do not have 100% of "assets", otherwise bank runs wouldn't be so catastrophic when enough people try to withdraw their funds in actual currency. Because it's not there. Your misunderstanding is that you're focusing on your average savings account, these types of accounts are inconsequential in the grand scheme of things, in fact many banks don't even want these customers since they can't make much money that way if at all.
Now as for credit it is not fully backed and they do create money out of nothing, any econ 101 course teaches you that. That is actually how most new money is created, though bank credits. The "money" is book money which is not legal tender, which means yes, they literally just make an entry into their books (today digital), same as Tether minting money out of thin air.
The most fatal aspect is that many people do not understand the complicated legal situation when giving money to banks. They imagine it like their money is sitting in a virtual safe just for them and the bank can't touch it. In reality once it enters the banks books you have lost custody of the actual asset (government money), which is why insurance is needed in case the bank goes under. In the EU for example all savings are insured up to 100k€.
>What Tether is doing, of course, is different, because they seem to create money out of nothing without having the assets to cover them
This is what banks do, you simply do not understand.
>"Sight deposits are an example of book money: sight deposits are created when a bank settles transactions with a customer, ie it grants a credit, say, or purchases an asset and credits the corresponding amount to the customer's bank account in return. This means that banks can create book money just by making an accounting entry: according to the Bundesbank's economists, ""this refutes a popular misconception that banks act simply as intermediaries at the time of lending – ie that banks can only grant credit using funds placed with them previously as deposits by other customers"". By the same token, excess central bank reserves are not a necessary precondition for a bank to grant credit (and thus create money)."
https://www.bundesbank.de/en/tasks/topics/how-money-is-creat...