There is no automatic download of collection to Kindles, whether collection is Starred or not.
Kindle for ios and I think Android — maybe Fire? — have a download all button that does this, but that is not and has never been a feature of Kindle.
Moreover there is no need to Star collections to be able to use them. They are implicit. If you Star them then they show up as items in Library mixed in with the books, but I’ve never used it (once it became optional with Cloud Collections). This thread is evidence that it is confusing. The mobile apps (and Fire) have a different way of showing them, and I like it much better (well. Kindle for iOS should let you sort the collection contents like everything else can.)
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