Desire for joint property - currently separated

Isn't that the same??

From today's perspective, maybe.
But when these words originated in their root, no. And somehow there's also a logic that one is basically the opposite of the other, so you just reverse the order.
But well, that's really off-topic now.

On topic:
What would I do in the OP's place? If there is a chance of renting out (and a further increase in value is to be expected), rent out the house and build anew with the partner. Before that, precisely agree on the equity contribution to be brought in and the annuity portions and the resulting shares in the land register. By the way, it is theoretically possible here to place a new charge on the house in the land register (virtually as an equity substitute) if necessary (to compensate for missing equity). At least up to the amount of the already repaid and thus freed first-ranking mortgage; depending on the increase in value and the disposition of the bank, a new second-ranking mortgage could also be beneficial.

Regarding paying off the loan: How long has it been running already? After 10 years, you have a special right of termination. Before that, definitely also upon sale, but with a prepayment penalty. If you don't want to sell but simply want a new lender, the bank doesn't have to accept that.
Have the prepayment penalty best calculated by the bank. Then you'll have clarity.

I see it a bit like Ybias. The whole discussion is, for my taste, way too factual and focused on the worst case. If it is already such a conceivable situation for you that you might go separate ways, and you both want to prepare for that, then I would wait with the shared property and sort out the emotional world first. For us, shared property only works with shared finances. We took out a loan in both our names, pay it from our joint account. I carried his child in my belly, he’s currently working full-time so I can accompany the little one in the first period. Family is give and take, and since I have my husband and my son in my life, I have only understood how little “I” and how much “we” I am capable of thinking. I had more capital for building the house than he did at the beginning. I put everything into the loan. Even if I had saved ten times as much, I would have done that. At the end of the day, money is just money, it has much less to do with luck than one might think at first glance. Maybe I just watched too many schmaltzy movies, no idea. Of course, there’s never a forever guarantee. But life is much happier if you prefer to assume the good rather than the bad.

There is absolutely nothing against that and it feels so good for you. For the other person, with perhaps different experiences or worries, the same situation feels different, but that doesn’t make either of them better or worse in my opinion. You can think of the worst case... and in fact you do once in a while, which is not reprehensible. One should also not expect the worst and certainly not be negatively oriented; at least that’s not how I am. What I find strange is a pigeonholing thinking that the one who worries and expresses it honestly is supposed to be the worse "lover" than someone else whose actual attitude we would only see if "unfortunately" it ever came to that. You go to the registry office, you change the tax class, you take on caregiving responsibility and much more, which I want to be able to rely on in a serious case (both partners). So why shouldn’t two people honestly think about this beforehand to prevent that someday in life NEITHER of them is left alone in the soup? I find that responsible and precisely a sign of love if both of us think about it. One does not exclude the other, nor does it make one the moral crusader and the other the greedy bastard. That’s too simplistic.

Maybe from today’s perspective. But when these words originated in their root, not at all. And somehow there is also a logic that one is basically the opposite of the other, so you just reverse the order.

Exactly! Sure, this version is also a good way, as long as it fits the two of them. I believe one would have to be in exactly the same situation to adequately evaluate all the circumstances. It would be nice if one were always just as clever with their own little problems. I’m working on it......

Why should two people not honestly think about this beforehand in order to prevent that someday in life NEITHER of them ends up alone in the mess? I find that responsible and precisely a sign of love when I think about it from both sides.

But especially if I want that later on NEITHER of them ends up alone in the mess, then it makes sense to also share what I have worked for as an individual in the past. To say "I already have a house here that almost belongs to me, but in case of separation it still belongs to me alone" is personally too strong an "I"-mentality for me for someone who plans to marry or have a family with the other person.
But how have others so nicely put it? Maybe I am a bit old-fashioned there as well.

I always say with these thoughts about the worst case (which I, by the way, also don’t feel comfortable with): "I know neither my future self nor your future self. We have to protect each other from these people." That the depths of the personality of today's selves often reveal themselves in such situations is an unpleasant but desirable side effect. From my perspective, a possibly painful but necessary exercise before one "binds oneself forever." And yes, all concepts that arise from this, be it a sophisticated prenuptial agreement with exclusions here and there or throwing everything together and trusting our future selves as well, have their legitimacy as long as both partners do not feel coerced and are treated fairly (or else both are treated unfairly to the same extent).

As far as I understood you, the crucial difference for you was that your counterpart didn't want any joint land registry solution at all

It was his house, inherited from his mother, which he already brought into the relationship (however, his ex-wife and their daughter still lived in the house, which is why we rented). In fact, it was never an option for him to put me on the land registry, that is correct.