Totally agreed that it opens things up to censorship in general and doesn't actually make kids safer. Charlie Jane Anders' The Internet Is About to Get A Lot Worse sets it in the context of book banning. The LGBTQ part is in the headlines because one big focus of the advocacy against it is highlighting that Democrats who claim to be pro-LGBTQ should not be backing this bill. This has been effective enough that Senators Cantwell and Markey both mentioned it in the committee markup, although it's certainly far from the only problem with the bill.
Sec. 11 (b): Enforcement By State Attorneys General covers this. It's hard to find -- the bill text starts out with all the text removed from the previous amendment, and if you click on the "enforcement" link in the new table of context it takes you to the old struck-out text. It's almost like they want to make it as hard as possible for people to figure out what's going on!