Is the main purpose of the Holy Spirit to testify for Christ and connect people to God?

I read a part in Gospel of John where Jesus said the Holy Spirit would come after him to testify on his behalf. I myself recently had an experience where I suddenly became Christian upon singing a hymn at the end of church. I never thought I’d ever believe in Jesus but after that experience (which I figured is “feeling the Holy Spirit”) it seems to align with Jesus saying the Holy Spirit would testify on his behalf.

It was like I instantly knew all the Christian doctrine was true and that my purpose was to take part in it forever. Is this a relatively common experience? Is this generally what the Holy Spirit does? Thanks