Thanks for the A2A.
The short answer is that nobody knows. We only have one example of life, and there are only so many conclusions we can draw from that.
However, carbon is the most suitable element for life. It is extremely flexible and has many stable forms. Some scientists have speculated about biochemical systems involving other elements, such as silicon, which also has a number of good qualities, but carbon is by far the best. If I had to place bets, I would lay my chips on carbon, although the actual specifics, such as codons and helical DNA are much more open to debate.
And proteins made of carbon need liquid water to do anything useful, so it does make sense that we start our search for life with Earth-like planets in so-called 'goldilocks zones'. But I agree with you that we shouldn't discount wildly different environments.