Just count how many coins everybody has before and after the loan and the only possible conclusion is that the supply has gone up. If you still maintain that that the supply has not gone up, you have a lot of explaining to do. This can't just be dismissed with a handwave.
The explanation is pretty simple actually: you created unbacked paper Bitcoin. Not a single new real Bitcoin was produced. The initial depositors no longer have the BTC they deposited, you loaned it out to somebody else. Yet you count their deposits as if they still own it, which they don't. It's a paper lie that does nothing to BTC supply.
You can write anything on a piece of paper, it doesn't affect Bitcoin supply. Miners mint new coins, nobody else.
Bank deposits are legally enforceable claims on money, which means they're... money, regardless of whether they are fully backed or partially backed by reserves. It doesn't make any difference. And the same applies to bitcoin deposits on exchanges, which are nothing more than legally enforceable claims on bitcoins. In other words bitcoins. Why are you struggling so much with this? I mean... it's pretty basic stuff.
You're the one struggling. You just agreed with what I said earlier: you did a swap from real Bitcoin (actual BTC that was mined and sits in a wallet) into a "promise" of said Bitcoin.
That doesn't increase the BTC supply. It's just shadow book keeping outside the blockchain. You made new "money", not new BTC.
Replacing an asset (reserves) with another asset (a loan) is not "shadow book keeping". But anyway... there is no such thing as actual bitcoins sitting in wallets. A bitcoin "wallet" is not a wallet but an ID. And there are no bitcoins either. There is only a transaction record of fictional tokens. These tokens (aka bitcoins) are created by appending an unbalanced transaction into the transaction record. This is shadow book keeping. But conceptually it shows that bitcoins are created with a simple bookkeeping entry. And more bitcoins can be created with the process that I described earlier known as fractional reserve banking. Again, this is all simple stuff that can be corroborated easily with minimal effort. This conversation is over as far as I'm concerned.
You can't do this with gold either, despite "paper gold". It represents more gold than gold above ground, yet still within supply.
Only fiat money allows you to create new money out of debt.