I saw it on American TV in the 90s or 00s. Pretty sure it was on TV and not from a VHS. I don't know if it was part of a show or one of those segments PBS Kids and Nick Jr had between shows. The library books open up and the kid jumps inside them. I think one is a forest or jungle and one is underwater and one is outer space but I might be wrong. The illustrations are drawn like a pop up book. The kid isn't a character I know - not any of the Sesame Street regulars or Arthur the aardvark or from Richard Scarry's Busytown.
It's not this one
https://www.youtube.com/watch?v=BP0Z1Uve4Fk and it's not the Between the Lions credits or the Reading Rainbow credits.
EDIT 8.22.23: It was about 2 or 3 minutes.