Do you introduce your s/o to your friends?

So my bf and I went to get drinks at a tea shop and one of the workers there was his friend, who I have never met. I was ordering drinks from another worker and she ran up and hugged him. She didn’t say hi or acknowledge me, and he didn’t introduce me to her either. I was kinda just trying to ignore them, because I already saw her starting to run up to him. I kinda got annoyed lol. I just stood there while they talked. For me, if we ever run into any of my friends, I would introduce them to him. If I ever saw my friend with their s/o, I would introduce myself to them, because I wouldn’t want to make them feel uneasy if they didn’t know about me, and I wouldn’t want them feeling left out. Am I thinking too much about this?