What insurances do I need as a homeowner?

For me

Are there any other sources for this?
I am quite sure that this is not the case. My sources confirm that as well.

w w w.cash-online.de/Versicherungen/2013/arbeitslosengeld-bu/159966
w w w.versicherungsarchiv.de/00428/was-geschieht-bei-ueberversicherung/

But your sources say exactly the same as mine:
“A proportionality should also be given here, this is usually queried and checked by the insurer in case of doubt. So it is also not worth taking out an excessively high insurance sum here, especially since in case of simultaneous reduced earning capacity (full or half) additional state benefits are provided and the amount of the insured pension naturally also determines the contribution.”

I had an appointment with my new financial advisor last week, and he also confirmed to me that the benefit of all insurances combined, which have to pay out in the respective case, may be at most as high as the net income, with some disability insurance policies allowing only 80% of that.

My old insurance advisor did not point this out to me, and I took out a disability insurance policy that would have replaced my full-time salary even though I only work part-time. In the event of a claim, I would therefore not have received the full benefit, not to mention if the pension fund had also paid me a disability pension for 100% occupational disability.
But I paid the contribution for the full-time salary coverage, and the insurance advisor also collected the premium for it.

The insurer’s check of proportionality often only takes place in the event of a claim, as with many insurances.

If you had read the contributions, you would also have read that there is no prohibition of enrichment in the [BU]. It may be that the insurance excludes reimbursing more than 80% and therefore asks what you earn. However, this only applies to the insurance and not in relation to other benefits, such as a disability pension. Nothing is considered jointly and therefore offset.

Your quoted sentence only says that it makes no sense to insure me with one or more [BUs] for 10,000€ if I previously only earned 3,000€.

I have taken out a disability insurance that would have replaced my full-time salary, even though I only work part-time

As I understand it, what matters is what the income is/was at the time the insurance was taken out. If you earn less at times, that is not relevant. The insurer does not offer to continuously adjust the disability insurance to your salary, which would also be nonsensical.