Hi @KatieSelf! That is an old article that applies to Cascade, one of the classic Esri Story Map templates, but your screenshot shows that you are using ArcGIS StoryMaps. Please note that editing the story data to add HTML is not supported in ArcGIS StoryMaps and may break your story.
Editing a text string in the story data using a tool like ArcGIS Assistant may work, but this is also not supported.
Since ArcGIS StoryMaps has draft and published versions of your story, you can easily get in a situation where you accidentally overwrite changes made outside the builder. Also, by editing a story outside the builder you are not following the expected publish workflow. This is likely why you are only sometimes seeing your text changes. Published stories are optimized for delivery by caching them on the web. Without republishing a story from builder the cache isn't getting updated, so you may not immediately see edits made outside builder.
For now, the recommended way to add "better" links (not just a text hyperlink) to a story is to use the Embed option and choose to show your embed as a card. Cards are nice looking links with a thumbnail, title, and description (screenshot below). In some cases, adding a hyperlink to some text in an image caption can also work well.
If there are features that you would like to see added to ArcGIS StoryMaps, please post or vote for your ideas on the ideas board so we can consider them for future releases!
Owen Evans
Lead Product Engineer | StoryMaps