Question for conservative and reform jews

I was raised in conservative Judaism and I have a question for others who were raised in conservative or reform Judaism. I frequently hear Christians characterize the difference between Jews and Christians as “Christians believe Jsus was the messiah, but Jews are still waiting for the Messiah”. I know this is a gross oversimplification for alot of reasons. Both religions have very complex lengthy and profound differences between each other. But even just the basic premise that we are waiting for a messiah is weird to me. Of course I know that we believe a messiah will come one day. But I grew up in conservative movement and have also attended reform synagogues. Honestly, I can’t remember any mention of a messiah in Jewish services or in my Hebrew school classes growing up. The only context for me knowing anything about the prospect of a messiah is because I’ve heard Christians say we are waiting for a messiah and I Google it or look it up in a book and say “oh yeah that is in there”. So the notion that we are “waiting for a messiah feels wrong”. The Messiah seems like a really obscure part of our belief system. I’m curious if this is the same experience for other people growing up in the reform and conservative tradition? Did your Jewish education spend any time on an expectation for messiah to come