I think the intended method for this is ‘copy view as image’, which will copy all of the map, including bits off screen. The data is in vector form so if you make a new document from the clipboard in PDF you should have a nicely scaling PDF.
However, in testing, the above method does take an image at the current zoom level (i.e. possibly missing some labels, etc.). I suggest you set your map zoom to normal and then ‘copy view as image’. From my tests here, albeit with different data, this should work.
TIL that the copy image method exports the whole map as rendered at the current zoom level and not at standard zoom as I’d hitherto assumed.