I will be graduating with a PhD from a US institution in computational sciences. I have published 10+ papers in peer reviewed journals in the field I am applying for jobs. I have been interviewed by some PIs, and after interview, I have been asked to submit a few hours of tasks for further evaluation. I was wondering if it is normal these days in hiring process to assign some work/test to evaluate the candidates on top of interview presentation. Anyway, I found the assignment interesting and have decided to work on it.
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.
Not everything that is weird is necessarily bad.
I'd love to hear from her why she does this. Maybe I'd be appalled.
My former PI used to give assignments to candidates he wasn't sure about but thought they might have potential. They would generally be small problems that he would then have one of his current students evaluate to see if 1) the general approach was reasonable and 2) how realistic their evaluation of their own progress was (e.g. knowing your results were poor was more important than getting good results).
He did this because his lab was relatively prestigious and got a ton of applications. He didn't want to limit his search to "only people from top 10 institutions" or "only people with publications in top journals" and he felt this approach gave talented people from diverse backgrounds a chance. It also made a sort of filter where if the borderline candidate didn't care enough to do the project, he didn't have to care enough to evaluate it. Since this PI expressed concerns about the amount of time you spent in your degree, they may have a similar mindset as my former PI.
Personally, I didn't find the projects that useful, at least for the candidates I evaluated. Maybe I was just a tough judge, but I generally found the candidates were less "passionate" and more "desperate" as the results I got back were generally higher effort than was being requested with an overly optimistic evaluation of their own progress. Still, it may have paid off for a talented person with a middling CV who wanted to make the move to a top tier institution.
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...
How does this project fit with the PI's research goals? The answer may be surprising.
Do you think this project would lead to a publication? Is it possible this project would lead to a note or other short submission? If so, go for it. Even if you don't get the job, you can submit a paper.
If it is a throw-away project, I would avoid it, unless you need the job.
And don't forget that you may be the top candidate!