I'd say one of the things you have suggested. Copying the license file from spegel into a SPEGEL_LICENSE file in the repository would be sufficient. So would be actually crediting the project properly in the README with something like "portions of this code were taken from the Spegel project, under the MIT license" with a following copy of the MIT license.
You could open the PR and it would also be faster than writing all these comments here about opening a PR.
That's not the point, it is not the author's duty to do that and him pointing out Microsoft's wrongdoing is meaningful at least to me because I will be more cautious if I'm ever being approached in a similar way.
> Microsoft's wrongdoing is meaningful at least to me because I will be more cautious if I'm ever being approached in a similar way.
That's the thing: Microsoft approaching the author has nothing to do with the wrong attribution. And I am not sure if the original author here is frustrated because of the wrong attribution or just because they would have hope money and fame from the fact that Microsoft reused their code.
Because it's not like Spegel lacks visibility (given the numbers they shared in the article), the link on Peerd's README is probably not bad for Spegel, and the attention here is publicity again. Probably infinitely more than if Microsoft had done the attribution correctly.