House purchase with full financing / hardly any equity / option: inheritance with debts?

she will not have the income in a few years that she still has now (then retirement...),

only because of her advanced age

Now I am really curious: what is considered advanced age combined with not yet being retired?
With your age, you could be my son... I just built a house...

she wouldn’t have a chance anyway to pay off the remaining sum of the house.

Well, if that’s the case: quickly sell off the place.

I am curious: don’t you see it too pessimistically regarding mom’s future?

And if she gives away her house and then still has to pay rent, is she financially better off?

Sorry, I don't want to step on anyone's toes here. But it is attached to the house. So it's not about gaining a fundamental advantage from it, but just about considering whether the combination "makes sense." From a cool perspective: Sure, she should sell the house. But she doesn't want to.

And if she gifts her house and then also has to pay rent, she is financially better off

Maybe she is actually better off because she no longer has to pay for necessary renovations herself, like, say, a new heating system. The income of the thread creator probably allows for that as well.
It's almost a bit paradoxical to take on the obligations for a second house just to reduce the interest rate for the first one.

To get back to the topic:
: What does your bank or broker say about the plan to finance both properties?

Mom's rental income must also be taxed. Maybe a gift with usufruct rights makes sense? So that she can continue to live there rent-free.

A usufructuary right significantly reduces the value of the property because it becomes much harder to sell. I suspect that with all discounts and the usufructuary right, the market value of the house will end up at about the same level as the outstanding debt. Then it is absolutely useless as collateral for the bank.

By the way, there are also quite a few tax matters to consider.