That is not correct; the tax exemption amount is only €500,000 for life partners and spouses, €400,000 for entitled children, and only €20,000 for everyone else.
The original poster (OP), the initiator, lives in Bavaria, where a normal single-family house with sufficient land often exceeds €400,000, so I find it very reasonable for the parents to start thinking about this now. Regardless of whether you plan to live in the house yourself or not. This way, you can save a lot of money because in the event of the parents' death, each child will inherit their share and, if the amount exceeds the exemption, will have to pay taxes. The tax office and inheritance law do not care at all whether you want to live there or not.
What I do not understand: did the brother receive the building plot from the parents as a gift, or why is he not included in the considerations? Is it documented anywhere that, if this is the case, the building plot is part of his inheritance? Otherwise, even if the parents would rather transfer the house to someone who will live in it, he still has a claim to the compulsory portion.
I now assume that you and the brother are on good terms and everything has been agreed upon to mutual satisfaction; in that case, I would DEFINITELY transfer ownership now. In the event of death, the statutory regulations apply if nothing else has been established in writing and notarized (will). Notarized in this case because simply written wills kept in some private drawer for emergencies are often challenged or suddenly disappear. I would not rely on that.
Now the parents can influence to whom and how much they transfer and possibly split the gift into two parts (I generously allow people who are only in their mid-50s another 10 years) to avoid inheritance tax and possibly an inheritance dispute.
And in all of this, it is completely irrelevant whether you want to move in at some point or not.
What I honestly do not understand is what business you have in this. I, as the testator, would definitely only leave it to my children, not to the (expected) sons-in-law or daughters-in-law. Over 50% of marriages end in divorce, and then the ex-wife and ex-daughter-in-law suddenly own part of the house. That would be an absolute no-go for me. Besides, your exemption in that case would only be €20,000 – well, maybe the garage...