It is true that in the event of a divorce she will receive the accrued gains. However, the accrued gains consist only of a monetary value and not of objects and/or real estate. In addition, the assets are evaluated as a whole, meaning the property is not considered separately. The accrued gain is calculated as follows: initial assets (assets minus debts at the time of marriage) minus final assets (assets minus debts at the time of divorce) = accrued gain. Each spouse receives half of the difference. The value of the property is indeed included, but the rest of the assets are included as well. So she does not necessarily get half the value of the house, especially if the mortgage is still running.
Without registration in the land register, your wife will not become the owner of the house. So she is supposed to help pay for the house with her assets, but none of it belongs to her. The accrual equalization, as mentioned, consists only of a financial compensation. Therefore, half of the house does NOT belong to her in case of separation; the house would belong to you ALONE even in the event of separation, and you would only have to pay her financially depending on the financial situation (accrued gain).
I cannot quite understand why you are considering not having her entered in the land register. I think that is unfair to your wife. Since she is supposed to bear joint liability for the debts, she should also own a share of the house. This is the simplest solution to better secure her both in the event of separation and in the event of death.
I am glad that you now want to give the real estate agent your wife's data as well. Also tell him what share each of you should become owner of (usually it is 1/2 each, but any other arrangement is possible). Real estate transfer tax, notary, and land registry fees will be incurred anyway, whether you get entered in the land register alone or both together.