The URL seems to only include either the page size or the page number, but never both. This is true for both logged in and logged out states.
https://meta.stackexchange.com/questions?tab=newest&page=2
https://meta.stackexchange.com/questions?tab=newest&pagesize=50
While logged in, the desired page size is saved and reapplied correctly, but logged out it's not.
This appears to be happening on every site with the new design.