Some explanation (I think):
Background
The page orientation in Writer is not directly assignable by formatting, even though it may appear so. The menu entry "Format - Page" (in AOO; aptly renamed "Format - Page style ..." in LO) does not insert any page formatting change at the cursor's position.
It alters the page style which is in effect at that point. This also alters other pages accordingly (assuming that they use the same page style).
The page style is by default inherited from page style settings active on previous page. To break this inheritance, first a page break is needed. This page break also does not exist as an individual entity (even though it may appear so from the way we "insert" it). Rather, it is a property of the paragraph starting the new page.
Page style is then a
subordinate property of
Page break.
The page break can be inserted explicitly (by the
Insert - Manual break ... menu item or by adjusting settings through
Format - Paragraph - Text flow) or implicitly (by paragraph style, the
Text flow tab).
What happened?
- If you copied content from a paragraph containing a "hard break" (inserted in paragraph directly, or in the paragraph style) with page style settings entered, this should carry over when you paste. The "operative content" in this case will be (part of) the first paragraph on your source page, and will constitute the first paragraph of the page after pasting.
- If you copied from a source where the page style setting was not present on paragraph level (no page breaks inserted; i.o.w. page style manually selected for the document, or inherited from the "next page" setting of previous page) the target page will keep the original page settings.