I saw a post like this a while ago, and since I was not having this problem I ignored it. But now I too am having this strange "large emoji" problem, so I thought I would share this and see if others are experiencing it.
When I receive emails from forum posts, sometimes, but not always, emoji's are blown up (see graphic below.) I checked to see if this happened to be something going on with my email client, and it doesn't see so. I check the email on my smartphone and in my webmail mail clients, and the emoji is oversized.
However, this doesn't always happen, it seems intermittent. Yes, weird. It seems that this problem started occurring somewhere around Moodle 3.5. I am running Moodle 3.6.1+ (Build: 20190111).
I will be doing more experimenting. I tried from my MoodleCloud, and everything was fine. I tried from my own moodle, and I am getting mixed results. Sometimes it happens and sometimes it doesn't. I don't know if it happens with original posts, or reply to posts. So I will keep experimenting, but I thought I would see if others had experienced this.
I did create a Tracker bug for this, MDL-64598.