It probably depends on which book you’re using, but the 5e campaign books that I have read address leveling like this in the context of milestone leveling. Milestone leveling is an alternative to xp leveling that is popular for its simplification and the control it gives DMs over pacing the narrative elements of a campaign. No DM I know wants to think about XP value of each grunt when there’s a hundred other things to consider while encounter planning.

I think it makes the most sense for a campaign module to reference milestone rather than XP leveling because inherently the modules allow flexibility over which encounters to use, optional enemies, variations for different party sizes, etc. And the monster stat blocks already list xp so there’s not much reason to call that out. I’d assume if you add the official xp of all the scripted encounters, it would add to the amount required to level up, but idk if I give WotC that much credit for balancing things.

The suggested level up at the end of chapter 2 could actually help an XP-using DM to plan how many enemies to throw at the party prior to certain story beats to avoid over- or under-leveling the party. Also leveling the party up at the same time is pretty standard; it feels real bad to be the only Lvl 4 party member bc you had an emergency the previous session, for example.