This is probably showing both our ages that this is new to you and very old for me.
I was on the web in the late 90s! I don't recall seeing anything like this, although it certainly may have existed. Animated cursors yes (CometCursor!), but not little animations chasing your cursor.
I remember copy/pasting scripts in dreamweaver to make leaves or snow fall on the webpage.
Clearly you were not on the web in the 90s. But agree it's very annoying.
I remember CometCursor and the like, but nothing that chased the cursor itself.