Append Documents but Keep Formatting

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If you have conflicting styles, I'm afraid there is no solution. LO Writer emphasizes styles to obtain a consistent look across documents. This culminates in the template concept.

From your description, your documents have deeply different formatting. Even in paper (=physical) typography, you won't bind together sections exhibiting disparate composition. The visual effect is ugly.

I understand that the difference of styles is an intentional feature (or maybe the consequence that harmonizing styles is too expensive a task). The best you can do is leave them as 2 independent documents and always handle them together (storing them in a dedicated director?). This is easy unless you have a technical reason to merge the documents, such as numbering sequentially items (headings, lists) or building a single TOC or index.

Without TOC/index, there is a standard workaround to achieve continuous numbering by forcing the number of the first heading in the second document but you must edit it manually in case the first document changes.

Note that even creating a master document importing your documents won't work because the styles used are those defined in the master document, in fact unifying the appearance.

When I have to do as you are describing, I use two sets of styles, for example Heading-A and Heading-B etc.. Then there is no conflict between the two documents.