It is, however, humanly possible, to run a real Postgres instance in a Docker container. You may use for example Testcontainers. So, I would not resort to an inferior Postgres "mock" for E2E testing.
For unit testing (also mentioned in the tagline of the project on GitHub) I could see you wanting something snappier than a real Postgres in Docker, so then... maybe? Purists of some following will tell you to use a mocking framework instead, but I think that something closer to the real thing would be better in all cases. This might be it, just be careful not to lull yourself into a false sense of security about how close to the real thing this is (isn't).
On first reading of the main GitHub page, I didn't take it that way. On second reading, I guess it could go either way. But there's talk about having reimplemented the network stack, so maybe that implies they just repurposed the rest of Postgres. I just don't know enough, happy to take your word.
The reality is that testing is as nuanced as anything else in software. Tradeoffs are different in different situations, and reasonable people can disagree about appropriate tradeoffs in a given situation.
It depends on the humans and what they're up to. Fast feedback is a very valuable attribute of a test suite, so reasonable people may well be willing to go down this road.
For unit testing (also mentioned in the tagline of the project on GitHub) I could see you wanting something snappier than a real Postgres in Docker, so then... maybe? Purists of some following will tell you to use a mocking framework instead, but I think that something closer to the real thing would be better in all cases. This might be it, just be careful not to lull yourself into a false sense of security about how close to the real thing this is (isn't).