So I know someone who recently took out exactly €40,000 fixed for 10 years at 1.5%, and he was significantly older than you. It is clear that the interest rate for such small amounts is always somewhat higher than, for example, for a €200,000 financing, because the bank's fixed costs have a disproportionate impact there.
You would have to take out a second loan anyway, even with the previous bank, because the loan amount cannot simply be increased since the interest rate level has changed compared to the first loan and thus different conditions apply, not to mention the revaluation of the house, the other income level, etc.
In principle, an additional collateral through the apartment to be purchased should of course lead to a reduction in the interest rate compared to if only the existing mortgage on the house is used. You simply have to compare what the cost of registering the mortgage for the apartment is and how much more interest you have to pay if you only use the already existing mortgage. For example, you can have a €30,000 mortgage registered on the apartment to be purchased (then the registration fees are probably not quite as high as for €40,000) and use the already existing mortgage for the remaining €10,000. Then the (remaining) loan amount would be about 75% of the market value for both properties. These €10,000 would technically be second priority, but if it is with the same bank anyway, this construction should definitely result in a lower interest rate than if you basically do a subordinated financing almost to the maximum (i.e., about 90%). It is known to me that rates drop significantly from a threshold of 80% financing.
But with this loan amount, in my opinion, it is questionable whether it is even worth the effort to deal intensively with these differences, since they should be quite small in absolute terms.