Is renegotiation possible for a home loan?

Worse still, due to the extension, the counter for the special termination right starts again at zero.

Correct, 2 more years of interest gained for the bank. As the saying goes, "the bank always wins." But okay, thanks to being clever, the customer is not disappointed but proud that he negotiated something out of the evil bank.

You are mistaken that the remaining term is 13 years. The TE was basically offered a forward loan with a 5-year term to be drawn in 13 (!) years. Try to find such a product on the market first...
As far as I know, the forward premium is currently 0.009% per month. That would be a 1.404% premium on the current 5-year conditions when disbursed in 13 years. So the offer is very good if it suits you.

1.8% for 15 or 20 years from today is not really impressive

Unfortunately, the comparison is very misleading. The difference is that when you conclude a new contract, you also take the money and start paying interest on it, instead of having the bank hold it for 13 years at their expense.

Calculating here is pointless. Do you really think the bank offered him an extension of 15, 20 or even more years and all at the same interest rate?

Calculating here doesn't make any sense. Do you really believe the bank offered him an extension for 15, 20 or even more years, all at the same interest rate?

Calculating here is the only way to seriously deal with the TE’s information. You and two other users just hammered at it generally instead of trying to engage with the topic. What’s that supposed to mean?

And now you’re dragging the topic into the troll corner by doubting the TE’s statement. Why?

Calculating here is the only way to deal seriously with the info provided by the OP. You and two other users only responded with general criticism instead of trying to engage with the topic. What's that about?

In my opinion, to calculate seriously you would need more numbers, which are not available. Also, it is a special constellation that certainly cannot be calculated that easily, especially since we do not know how the bank refinances.

And now you push the topic into the troll corner by doubting the OP's statement. Why?

I am not pushing this into the troll corner. However, I do doubt the statement that the bank charges a flat interest rate for such a special constellation for 15, 20 or even longer fixed interest periods. I doubt that based on my professional experience.
That has nothing to do with just attacking.