Depends on the instance in my experience - mastodon.social usually posts within seconds. Note that due to spam issues, kbin.social has been dealing with a recent wave of defederation, so if you're not seeing your posts appear, that might be the cause.
@readbeanicecream Hashtags are really hit or miss in general across instances.
I found that most Mastodon instances only collect posts from other Mastodon instances under hashtags (definitely the case with mastodon.social). I suspect this is because they are sharing the same posting format.
The long form posting format that Lemmy and Kbin use for Threads has a 25k character limit, too big for most Mastodon instances. This long form post is truncated into the posting limits of the Mastodon instance, but the conversion protocol is not sophisticated enough to read the JSON file to flag the enclosed hashtags as data fields defining the post.
The user-facing presentation layer then adds hyperlinks to what it can determine as hashtags (as it does to anything with a # preceding it), but the federating instance itself thinks the entire post is just post content.
Related notes - I found that when posting to Kbin from Mastodon, the order of the hashtags determines which Microblog the post appears under. Also, Lemmy strips hashtags placed in the "Tags" section of a Thread or Link when content makes its way there.