I'm writing this post only because I get fascinated by the etymology of words and their usage-journey through history and cultures. It's not meant as an obnoxious "hmm actually..." ^_^
That said. As far as I understand...
According to the english Oxford dictionary (but also the italian Treccani) a messiah is literally "a charismatic leader" specifically coded as a "saviour" of people/nations.
So for example the use of the word messiah in religious contexts is common not because a messiah is a religious leader, but because most religious leaders promise/represent "salvation". It's not, in its origin, a religious word. The actual ancient hebrew etymology is even more generic, only meaning "chosen one" or "anointed one".
Also, in my personal experience consuming movies and novels and articles and common parlance I have always encountered the word messiah used exactly in this way (charismatic saviour/leader), also outside of religious contexts: dubbing Elon Musk as the messiah of electric cars :P
While I have never heard of its use as "god incarnate" ... for that I would usually think of the word "avatar".
But I can imagine how in christian tradition there could have, in time, been a mismatch... as the word "messiah" got transliterated to "christ" (same meaning, different root language) but then because it is applied exclusively to Jesus, and Jesus is the son of God and God the son, then meaning-A washed on to word-B although word-B has its own meaning.
Or, am I missing something? :)
(could be, happens quite often XD )