How can I stop the full HTML editor from deleting my  paragraph?
Could be related to the auto paragraph funcitonality of CKEditor, which is used by default and can be disabled with this !deprecated setting:
&quot;autoParagraph = false&quot;

This can be easily disabled using the ckeditor_config module, see https://www.drupal.org/project/drupal/issues/3131055 for more information.
The whole paragraph wrapping in CKEditor is kind of buggy, you could also try these patches: https://www.drupal.org/project/drupal/issues/2876094 (but there the problem is an added p after an img)

I had some troubles when using linkit: https://www.drupal.org/project/linkit/issues/3162596 and made this core issue https://www.drupal.org/project/drupal/issues/3162605 (this is not related to your problem as your using the align and caption filters - but you see where the magic happens - on Drupal side).