Potential Postdoc advisor giving exams (assignment) as part of hiring process
It is highly unusual. As you note, the PI has plenty of "standard" information (publications, recommendation letter, CV, etc.) that can be used to assess your potential as a collaborator and independent scientist. This is what most PIs will use in the hiring process. Some will ask you to give a seminar or do an interview by phone, video, or in person.
How the PI evaluates you as a candidate will reflect how the PI evaluates you once you are an advisee. This is especially true if they ask you to do something unusual, which is certainly the case here.
You are being told that the work you have done in the past, the good credit that you have earned with your previous advisor, your attendance and interaction at seminars... these are unimportant factors compared to whatever skills this "exam" is testing. It sounds like you do not agree with that attitude. That is reasonable, and if true, I suggest that you and this advisor may not be a good match.
I find it a bit intriguing, actually. Though unusual. And, of course, if you object to it, move on now without another thought.
But perhaps she just wants to know how you will attack a new and fresh problem without the support you may have had in your studies. Or perhaps she and you are in a field in which a lot of opportunities pop up and there are threads of potential research that need a quick study and overview.
I don't find it offensive. Painful to comply with, perhaps, but that is up to you. Once she is paying you such things might become a requirement, not a request.
And I don't agree that she considers your accomplishments unimportant. But if the competition for the position is fierce, she will want every bit of information she can gather on candidates.
There is no reason to do this, unless you want the position, and no reason not to, but for the time it takes, if you do.
You choose.
Not everything that is weird is necessarily bad.
I'd love to hear from her why she does this. Maybe I'd be appalled.
In the professional world there are plenty of interview processes that contain one or another way of skill assessment. That's pretty normal and not a way to devalue your general expertise but a matter of establishing whether your skills do fit the exact needs of the company and typically also if your way to apply them fits the company culture / type of person the company is looking for.
Whether an exam/report is the right and (e.g. wrt time investment) fair way to check how well you match for the given position is certainly debatable and definitely uncommon in the academic world. However, note that this does not mean your other qualifications do not matter, they are the basis on which you get to the test level. Whether the job is worth the involved effort only you can decide.
On the other hand, isn't it a bit odd, that you want to complete the report while you don't want to take the position either way? That wastes your time and that of the potential advisor who will likely read it. Then again, if it is so motivating to do for you, maybe it is the perfect check whether you bring the right kind of motivation with you for the job. And it can also be valuable to you if you know the kind of stuff you would later deal with on a daily basis...