Using o4-mini-high, it actually did produce a working implementation after a bit of prompting. So yeah, today, this test passed which is cool.
However, looking at the code that Gemini wrote in the link, it does the same thing that other LLMs often do, which is to assume that we are encoding individual long values. I assume there must be a github repo or stackoverflow question in the weights somewhere that is pushing it in this direction but it is a little odd. Naturally, this isn't the kind encoder that someone would normally want. Typically it should encode a byte array and return a string (or maybe encode / decode UTF8 strings directly). Having the interface use a long is very weird and not very useful.
In any case, I suspect with a bit more prompting you might be able to get gemini to do the right thing.
OTOH if you tell it to write a Base62 encoder in C#, it does consistently produce an API that can be called with byte arrays: https://g.co/gemini/share/6076f67abde2