What can I do with a research project that is my university’s intellectual property?

First, it would be good to know if that is a claim they can legally make where you are. It is possible that it is an empty claim.

Second, if it is a proper claim, you should learn how it is interpreted by the university. A place making such a claim should have an office at which you can learn the consequences. I suspect that all it means is that you need permission from them to publish and, perhaps, include a reference to the university in the acknowledgements.

But forbidding publication would be unlikely except in extreme circumstances and assigning it to another "author" would be unethical.

My guess is that you have a way forward for nearly any sort of publication. It is actually to the university's benefit to have students publishing.

As Buffy says, it's very likely that you can publish your work. What you should do is discuss this with your project advisor and probably have them as co-author, as I assume that they had a role in the project, right? Additionally they are certainly able to help you make the publication more likely to be accepted.

Institutions usually retain (some) IP rights on the outcome of students projects because such projects are part of the curriculum and usually include work done by the professors; sometimes the main idea is actually based on the professor's research topic. But this is not meant to limit your ability to publish, it's mostly for the cases where the project could lead to a commercial application based on the university/professor IP.

This is something you should have checked before signing any contract as student/employee at this university.

Certain legislation give more intellectual rights to scholars / teachers in some places than others.

Things like "Academic freedom" or "University teacher exception" clauses may exist in the IP legislation of your country.