Section Break - continuous doesn't alter page numbering and should not affect headers and footers.
Make sure that all footers have 'Same as previous' at the right hand end, when in header/footer view.
Start with the footer on the last page and work back using the header/footer toolbar 'Show previous' icon. Every footer should show 'Same as Previous' until you get to the first.
If you put page numbers in the first footer you should then have them on every page.
I just used the 'Insert Auto Text' and used 'Page X of Y' in the first footer and the page numbers appeared right through to the last page, despite using page breaks - both continuous and next page types.