Is it allowed to use Stack Exchange to find people who would like to work on a project?
I am basically looking for students who are interested in creating something to show to future employers.
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Is it allowed to use Stack Exchange to find non-paid Experts?
I need a Tool to manage Projects (like this one) in a completely traceable fashion.
I too was interested in that at one time.
You say "No Tool currently available completely satisfies my needs", but there are many such applications already, see e.g. https://www.capterra.com/requirements-management-software/
Is it allowed to use Stack Exchange to find non-paid Experts who work on the project solely out of passion and their love for knowledge?
It is offtopic on any existing SE site (see https://stackexchange.com/sites)
And it goes against how SE sites work.
And trying to find unpaid people, working on solving your problem, that is uninteresting to them is going to fail. And in field of programming there is plenty of paid or interesting or paid and interesting projects.
If you want
Tool to manage Projects (like this one) in a completely traceable fashion.
you will likely need to pay someone to do that, if all existing ones are somehow insufficient.
You can try to recruit people, but do it outside SE and in places where you can expect volunteers, with more time than ideas (an university project?).