Currently Network Notes (ActivityPub) don’t support hashtags. You type #something and it renders as a plain text, not as a tag.
This is a big problem from a Fediverse perspective because hashtags are a very important tool to be discovered. The Fediverse has algorithm that serves you suggestions. Everything comes from the people you follow… and the tags you follow too. Given that Ghost blogs / newsletters are thematic by design, these tags are key for being discovered beyond the followers of your followers, in more distant and at the same time thematically direct connections. Anyway, you get the point and you surely know this already. 
If the Ghost team doesn’t have this feature in your plans, would you accept a patch implementing it? I’m not a developer but if the cost is not crazy I would consider finding the means to pay someone to develop this critical feature. Many open source ActivityPub clients support hashtags and I guess that will help the implementation for Ghost.
Ghost tags in post have the same problem, but I don’t know if, technically, they require the same solution or something different. For me the bigger problem are the lack of tags for pure Notes, because it seriously hampers the effectiveness of the Network promise.
By the way, this was reported by @DreamWave as a bug, and therefore it was closed automatically after a while.