Taking over half of the house after separation - questions about options

Unless a partnership agreement (for a GbR according to §§ 705 Building Code, where there is the so-called settlement according to § 730 Building Code) has been concluded, two persons with initially joint pursuit of purpose (= housekeeping, i.e. without a partnership agreement) at least legally form a "community" according to §§ 741 ff Building Code. And for example, § 755 Building Code applies:

§ 755 Building Code - Correction of joint debt

(1) If the partners are liable as joint debtors for an obligation which they have to fulfill according to § 748 in proportion to their shares or which they have entered into for the purpose of fulfilling such an obligation, each partner may demand, upon dissolution of the community, that the debt be corrected from the communal object.

(2) The claim may also be asserted against special successors.

(3) Insofar as the sale of the communal object is necessary to correct the debt, the sale must be carried out according to § 753.

Another question:
Is there a loan agreement with the ex-girlfriend?

There is the joint loan agreement from the bank, that is all. And of course the purchase agreement from the notary.

Hm, if I were the ex and someone told me that I should simply remain liable for a few more years... wouldn't it then be worth considering selling my share to a third party?

I wouldn't find either option very classy!

How am I supposed to understand that? You mean, that

My comment referred to the one from Fuchur directly above. I think he wants to lean towards delaying the Ex, which I wouldn’t consider particularly good.

My comment referred to the one by Fuchur directly above. I think he wants to stall the ex, which I wouldn't find particularly good.

No, that was not directly my intention. Although I can imagine that the OP also "doesn't find it particularly good" to have to scrape together €25K just to return "her" share.

Besides fundamentally questioning both parties' positions, I especially wanted to challenge what "her share" actually is. It is completely taken for granted that we are talking about the money she paid for the purchase. She did not lend money that she wants back, but rather entered into a financial/liability/risk structure from which she also generated value through the residential use. Who would stand up and simply claim that SHE has to repay his full loan share and get the house in return?

Whereby she could then charge you rent for her part

Well, if one cannot come to a reasonable (!) agreement (the OP said nothing about the emotional side), then in the extreme case it comes to a sale and both end up as losers. One should keep this in mind and at least try an emotionless, reasonable, and "fair" solution before more debts are added to the house and several consumer loans and one's own air grows increasingly thin.