Glad I could help somewhat.
Another area of research (but I doubt it would fit in a 4-5 month program) is static type checking.
As far as I know the first paper in that field is this one by Marlow and Wadler.
The Gleam project is exploring the topic. I may be wrong, but I believe people at emqx are exploring something in the same vein and the people at Facebook WhatsApp are working on some typed erlang thingy (but I know close to nothing about that).
Given your timeframe, I still think working on some nice CRDTs would be both realistic and nice for the community.
Again, please check with your teaching staff. The elixir community is great, but having in person advice from the people who will ultimately judge your work is better.
Also, while I certainly think you should strive for excellence, if you can’t provide a production ready library, it’ll still be a great addition for the elixir/erlang community if you document your motivation, hurdles, and choices.
All that to say don’t burn out as a student, have fun learning, it won’t be useless (even if whatever lib you decide to implement isn’t used). At the very least you’ll gain some expertise that you’ll be able to leverage to help the community in the future.