There seems to be some inconsistency with recognizing pre-existing iMessage apps as stickers vs. apps.
I have two sticker packs, both from the same developer, not tied to any installed iOS app. One pack the system automatically recognized and moved it to the Stickers section. The other pack remains as a separate iMessage app.
What’s interesting enough is both packs have a custom search field built in. In the pack that’s recognized as an app, search works fine. In the pack recognized as a sticker, it shows the text saying “swipe up to search” but there’s no actual way to activate it.
I’m guessing developers will need to go in and adjust their currently existing sticker packs to make sure they register as stickers and not apps. iOS doesn’t seem to do a good job of doing it on its own.