What is the most idiomatic way to let clients edit phrases in HTML?

Are the banners related to each page? If so, I would use a custom field or just a metabox that the user could edit or enter information into on the page that you want the banner to show up. The field would show up below the content in the page editor. You would then in your single.php add the code you noted above to encase whatever is typed in the custom field.

If the banners are NOT related to individual pages. I would make a custom post type “banners” and then have them randomly show up on pages by inserting a call for the CPT within the single.php.

You can either use a plugin to create the fields or these reference links will help you get started on creating your own:

https://codex.wordpress.org/Plugin_API/Action_Reference/add_meta_boxes
(explanation etc)

https://developer.wordpress.org/reference/functions/add_meta_box/ (code examples and usage)