I’m a long term (and now pro) Drafts user who also uses Bear App.In the share sheet on my iPhone and iPad I can ‘save complete webpage’ with Bear and it’ll save a text version of the webpage I’m on.
I think my share extension setup is still set as the default. It’ll include any selected text. So if you can select all the text and then trigger the Drafts extension, it should get you what you want.
Failing that, if you used something like Apple’s Workflow app, that could be passed the details from the share sheet Workflow extension and then push the text into Drafts.