Description of the need
When adding a context by path, every field available to the context is presented in the dialog box. This not only produces un-necessary clutter but creates a bad UX because the field chosen may be attached to a different entity type, making it easy to accidentally add a similarly named field that won't display data as expected because it doesn't belong to the given layout path provided in the context.
Additionally, not filtering on a given criteria might also a performance hit on larger sites that have hundreds of fields. By limiting through the selection rule, it reduces the number of fields that need to be loaded.
Proposed solution
Add Selection Rules so a context can be limited to only show the fields related to the rule.
Alternatives that have been considered
See the Drupal Panels module Selection Rules for more inspiration.

Recent comments
Hi! The description is still very vague and lacks step-by-step instructions on how to reproduce. It doesn't include the version of Backdrop either, nor a list of contrib modules you are using...
Problems with HTML content and text formats
Sorry, it did seem confusing when I read it back... So if I add some html to a text field, for example in a page or a block, whatever the text format of the field may be (raw html or basic...
Problems with HTML content and text formats
Could you please post clear, step by step instructions to reproduce the problem? Your first message refers to HTML content, and your second to text formats. Please add details to reproduce each...
Problems with HTML content and text formats