Thanks for the inputs. But regarding @JPBergsma 's response, I still find that there is little to no time difference between both of those queries. Both of them being really slow still.
Lastly regarding the comment of @ml-evs about the query to obtain Li-Co-O structures (?filter=elements HAS ONLY "Li", "Co", "O" or ?filter=elements HAS ALL "Li", "Co", "O" and nelements=3. My intention is to find all phases in a composition range, but also including the edges of the phase diagrams. Meaning that I am inputting which elements appear for sure in the phase, and which may or may not appear. So if I mark Li and O as ‘sure’ elements, and Co as ‘may appear’ element, then it should return all phases containing Li and O (Li2O, Li2O2…) and also phases that include Co (LiCoO2…).