Do you know if the "Michelson-Morley educational kit" is really enough to achieve the accuracy of the original experiment or is it just to make "any" functioning interferometer?
I'm pretty sure it exceeds the accuracy of the original experiment. I think not being based on a trough of mercury is pretty important as well. But the manual shows several types of interferometers that can be built in lab courses.
Still, I see it is actually called "Michelson Interferometer Educational Kit", not "Michelson–Morley" and the user guide I'm reading (your link gives "The resource you are looking for has been removed", so I've clicked on the "User Guide" on the page instead) also takes care to never directly mention Morley or to suggest that the same experiment can be reproduced with that kit.
Not my field, but my understanding is it's called the Michelson Interferometer because he designed and built the first version a few years before the famous MM experiment for the purpose of measuring the speed of light. See the diagram on page 3 of his 1881 paper "The relative motion of the Earth and of the luminiferous ether" https://zenodo.org/record/1450060 (note this is before the collab with Morley)
Edit to add: I just noticed a fun thing in the conclusion of that paper "In conclusion, I take this opportunity to thank Mr. A. Graham Bell who has provided the means for carrying out this work..."
Do you know if the "Michelson-Morley educational kit" is really enough to achieve the accuracy of the original experiment or is it just to make "any" functioning interferometer?