As of 2023-05-23, the #Hashtag and @Mentions indexes are deprecated and are no longer available.
The hashtag index isn't very valuable since the overwhelming majority of content in Geminispace doesn't contain hashtags. Using a general search engine does a better job at finding content about a specific topic. It's possible I may use #hashtags on a page as part of the process to index content on a page for the search engine.
The @mentions index doesn't provide a lot of value either. They are primarily used inside a specific capsule (Station, Midnightpub), or a pubnix. These capsules typically already provide a way to see all mentions of a user. Cross-capsule mentions are rare, and are usually discoverable via general search anyway. Furthermore, detecting @mentions is often prone to false positives.
Finally, these indexes predate the Kennedy search engine. They were statically generated files, slowly updated, and a bit of a pain to maintain. This, coupled with the low overall value and the ease of getting the functionality otherways, is why I'm deprecated these indexes.