To add one datapoint: I actually installed LibreOffice just now just to try it out. I went via

Format > Page Style > General [this tab was open by default] > Orientation: Landscape

If that is the correct way, then it was, IMO, hard to miss and fast to find. If it was the wrong way*, however then I’d say I find the menu labels misleading.

*I am not quite sure, because the dialogue had the Title “Page Style: Default Page Style”, so I would have expected pages in all new documents to now start out in landscape orientation, but I opened a new document, and the page was in portrait orientation. So, I think I did what I tried to do - change orientation only in the current document - in spite of that (misleading, thus proving your point?) dialogue title.

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