

It is worth knowing exactly what a swap service observes when you use it — not the marketing version, but the honest inventory. That knowledge lets you judge the "no-logs" claim sensibly and shrink your own footprint regardless of what any service promises.
To perform the swap at all, the service handles certain data by definition:
None of this is sinister; it is the minimum required to move coins from one form to another. The question is what happens to it afterward, and how much of it you handed over unnecessarily.
A properly non-custodial swap is structurally limited:
Most of what a service "could" know is actually up to you:
A swap service sees the deposit, the destination, the amounts, and — if you let it — your IP. It does not hold your funds or your identity unless you provide them. "No-logs" governs what it keeps of the unavoidable data; Tor and minimal disclosure govern how much unavoidable data exists in the first place. Control the second, and the first matters far less.