bsky.app/profile/adva...
It would be possible to make the client save a copy to your PDS when you save a post, but that would make them not private and probably annoy a lot of people regardless.
interesting that Bluesky calls bookmarks "saved posts". when we were building bookmarks at Discord, we considered calling them "saved messages", but we went with "bookmarks" because we thought "saved" might imply that it will store a copy even if the original message gets edited/deleted