So sometimes I want to share a post without adding any text to it, but I add tags for the sake of anyone wanting to filter out things that I share, and my shared post shows up separately under the site-wide tags that I've added to my rechost. Not only does this clog and tags that both myself and OP have added to to the post, but also I'm not sure it's such a great idea for someone who's sharing a post to be able to add a post into a sitewide tag that OP didn't choose to post it into.
It makes more sense for a rechost to show up separately in the tags if the person sharing has actually added to the thread, so I guess maybe what I'm suggesting is that rechosts should behave differently when there's no text added to the headline or post body fields? Idk, I appreciate the way that Pillowfort lets me add tags to shared posts without then adding said post to the sitewide tag, but a big difference between Cohost and Pillowfort is that the latter doesn't really have threading, so I'm not 100% sure what the best solution is given the way that threading is supposed to work here
Agree with @Silver that the best option here would be to only put posts into tag search pages if content was added, so that users can organize posts on their own page without every share of a post clogging up the tag page.