Baukindergeld - Family Constellation

That is not correct. Only the applicant must be (co-)owner of at least 50%.

Where does it say that? The partner is out of the project.

And a life partner is not the domestic partner, but the same-sex life partner according to the Life Partnership Act (predecessor law to marriage for all)

I see less of a problem there.

The house must be owned at least 50% by the applicant and/or partner. Fits.
Children under 18 years must live in the household, they can also be the partner’s. I have not yet read about a restriction to biological or adopted children.
“KfW” also defines “partner” as “life partner.” Also fits.

Just call the hotline.

Where does it say? The partner is out of the project

Information sheet of the KFW

Who can submit applications?
Any natural person,
who has become (co-)owner of self-used residential property and
who is entitled to child benefits or lives in the same household as the person entitled to child benefits and
in whose household at least one child is registered who has not yet reached the age of 18 at the time of application and for whom there is an entitlement to child benefits in the household and
whose taxable annual household income does not exceed 90,000 euros for one child, plus 15,000 euros for each additional child. The child must meet the above conditions

And a life partner is not the domestic partner, but the same-sex life partner according to the Life Partnership Act (predecessor law to marriage for all)

I agree with you that the "life partner" probably does not mean the colloquial domestic partner, but the life partner according to the Life Partnership Act.
However, the original poster will live with the partner in a marriage-like community.

Quote also from the KfW information sheet

Applicant and child
As an applicant, you must be entitled to child benefits for the minor child living in the household or live in the same household with the person entitled to child benefits (spouse or life partner or partner from a marriage-like community)

Again about the funding goal of the Baukindergeld

The KfW and the Federal Ministry of the Interior, Building and Community promote with the grant the first-time acquisition of owner-occupied residential property (single- or two-family houses, condominiums) for families with children with the goal of building home ownership. The Baukindergeld has the policy goal of increasing the very low home ownership rate of families in Germany in European comparison.

The definition of "family" was debated for a while in the grand coalition, since some pale-blue backward people only wanted to see married couples there. Politically nowadays, of course, untenable.

If you separate, you will continue to receive allowances nicely

No, because then the funding conditions are no longer met. This is subject to registration and punishable by law.
No different than in the case of divorce.

Once again, he is the sole owner! Nothing to do with money!

Again, he is the sole owner! Nothing to do with money!

Do the ownership relations matter? I don't think so.

He is the sole owner again! Nothing to do with money!

Irrelevant. see above. The applicant must be the owner, and this applies here. The children living with him do not have to be the applicant's.