Paying "rent" to the partner... how?

And what will you do if the owner simply changes the lock? What you are doing is a lot of theory. In practice, it’s different.
He buys, so he should also pay for the house. And that 100%. The interest is negligible anyway, most of the installment is HIS asset building, which you would be financing.
Contribute sufficiently to living expenses and that’s it. No stress.

Well, no stress. If his mother finds out that I’m living there “for free,” oh dear.
But yes, I think I’m overthinking it. If things get messy, even a rental contract is probably worth nothing.

What do you want then?
That you break up and you continue to live in his house? Hardly realistic.

No, just one month (or 3 or x) notice period to find something new.

You should simply bear a higher share of joint costs, e.g. groceries or the vacation would be on you. Since he alone bears the housing costs.
That would be a form of compensation. I thought that’s what it’s about?

Yes, it’s about a fair division of costs, which also takes the future into account (keyword asset building).
I might have misunderstood this "higher share," but I thought you meant that I pay in more overall than he does.

Hypothetical:
Loan costs: €1,000 (he)
Additional costs: €300 (me)
Groceries: €400 (me)

Then I would have €300 left to provide elsewhere.

Would you find that fair?

No, I wouldn’t find that fair

He 1000 minus interest for asset building
You 300 euros asset building

No, I wouldn't find that fair He 1000 minus interest for wealth accumulation You 300 euros wealth accumulation

The approach is good

Specifically, if you really want to share everything correctly:
He finances €300k at 1% interest = €250 monthly (since it is an annuity loan, the interest decreases monthly).
Share the amount = your basic rent
Share the additional costs
Share your living expenses
Repayment on the financing is his asset building.

Conclusion: Your contribution to the property financing is almost negligible. If you pay more than half of the interest costs, you are losing out.

Well, one could say: I 300 € plus whatever else I would have to pay more in rent.

If I lived alone:
Rent 600
Additional costs 100
Groceries 300
Asset building 300
Total 1300

With him:
Additional costs 300
Groceries 400
Asset building possible: 600

Well, you could say: I 300 € plus whatever I would otherwise have to pay more in rent.

You could. Then you are financing his asset accumulation. If you want that, then do it. The fact is, you live together in HIS house, for which YOU then provide the repayment. I don't care, but you asked. Anything that is more than half of his interest costs you might as well burn. The result is the same for you. However, I wonder why you even ask if you don't want to hear an objective result?