There seems to be a problem with the custom post type feed support when has_archive is false.
Check for example these tickets:
- #16415 Don’t require CPTs to have archives in order to have feeds
- #24867 Feeds for custom posts type can not be set independently of has_archive and supports => comments
So regarding the native support, it looks like you might have to settle for has_archive as true, while these tickets are open 😉
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