ADDIN EN.CITE is only the type of the fields. They have a text value (what is under the gray shading). Since Writer doesn’t recognise the XML tags, it simply ignores them, effectively transforming what should be managed by the add-on into ordinary text. But, due to the XML field extent tag, the value ends up protected.
I am not aware of any simple means to remove protection. A work around is to double-click on a field to select it and copy. You can then paste the value anywhere and edit it.
This will be a lot of work. You must design your own collection of paragraph styles, character styles and list styles. Apparently you have no fancy page style, so you can go with Default Page Style. The biggest task is to analyse the text to see the various semantic categories of paragraphs (each category ends up into one paragraph style). For the main discourse, use built-in Text Body. For numbered headings which open a new topic, use Heading 1 and other Heading n if you have subdivisions.
Most of the outline seems to be made of a multi-level list (at least 3 levels). These could be covered by a single paragraph style associated with a single list style (a misnomer because it only describes bullet/numbering properties and level indentation). You change level by typing a Tab at beginning of the list item to change for a deeper level. The reverse is Shift+Tab.
Once you have your paragraph styles, apply the ad hoc one to a paragraph then remove the existing direct formatting with Ctrl+M (may need to select whole paragraph in case there is also character direct formatting). Special emphasis on words should be handled with character styles like Emphasis (italics) or Strong Emphasis (bold).
The remaining issue is the bibliography. Either you consider your document as frozen and you can make do with present ordinary text extracted from the fields, or your document will be later updated. In the latter case, you should rebuild the bibliography with the built-in tool.
Note that this restyling will only be guaranteed to be stable and reliable only if you save .odt.