Page numbers pulling from the default template all appear on the left side of the page.
How do you get the page numbers on a left page to appear on the left and the page numbers from a right page to appear on the right?
I think that, after editing the default template, copying left to right changes the location of the page number token so that it matches the left one rather than alternates.
The default template isn’t ideally designed for this. It’s better to extend the page‑number frame from margin to margin (the default alignment of the Page Number Paragraph Style will then give you the result you want).
Then it won’t be a problem to use L>R or R>L.
And the other solution by @asherber below reminds me that once your frame is resized, you should set the anchors that way before pressing L>R:
Now in the Properties panel, change the Right measurement to 0.
Edit:@charles_piano slipped in first with a different suggestion. There are advantages to doing things that way, but also some potential hassles with overlapping text frames.
I think there is an easier way for this, at least I use it. Yes, in the Page Template Editor make the text frames span the whole page.
The crucial bit: when you input the page number token, choose the dedicated “Page Number” Text Style.
This text style places the page numbers automatically to the left and right outside edges of the frame.