Is the dream of a home realistic with our financing?

It reads as if someone is trying to sell you a lot, so compare it with other options, e.g. just KfW and annuities, and see what you have paid/left in debt after 10 years including all costs.
If you manage with 180,000 and 5% repayment using annuity/KfW (interest rates are low), then without special repayments there is less than 90k left after 10 years, which is no longer a big "risk".

What are the installments per loan and how much do you want to put into the [Bausparer] and under what conditions? I also think the pure annuity option should be cheaper.

A pure annuity loan will probably be cheaper. "Bullet loan with repayment substitute funds" usually only makes sense for landlords, especially in the current interest rate situation, a normal annuity loan + proper repayment is usually the better choice for owner-occupiers.

That the savings bank advisor also recommended you term life insurance and brought up the topic of occupational disability is basically positive. Both are very important issues to consider when financing a home. Just do yourself a favor here and compare very thoroughly between different insurance companies, especially with the occupational disability insurance, details matter. An insurance broker or a consumer advice center can possibly help you here.

Without going into detail now, one question: Kfw 70 or 55 or PH?

Overall, it reads like a good deal, just unfortunately not for you. A lot is included here for which you unfortunately pay heavily and your bank earns well.

In addition, a short [LZ] and poor interest rate. So please obtain further offers and negotiate hard.

Installment amount 877 € plus 280 € for the building savings

Yes, that should no longer be a problem with today's financing options. It will work.