The first example multi_page_sync_components shows how to synchronize component values between pages. This example is an alternative way of synchronizing an input parameter common to many pages, obtained through persistence instead of dcc.Store as in https://github.com/AnnMarieW/dash-multi-page-app-demos#13-multi_page_sync_components
The second example page_sync_with_query_strings adds query string capabilities to the first; if you append ?year=2100 to the URL of page 1, 2 or 3, you will see the year parameter being set accordingly.
Unfortunately it seems that there is a bug in persistence management, in fact persistence works fine (as in first example) until you don't use query strings; but after you apply a query string, as soon as you change page (and only the first time you change page after applying a query string) persistence is not able to keep the current value and initial value comes back, even if it should come back only on page refresh (persistence is of memory type).
From information printed on console by the line
print(year,hasattr(config.app_spanning_input, 'value'))
you may see that the code follows the same steps regardless of query string being applied just before page change or not, but the result is different, meaning that Dash persistence is unable to keep the current value as expected under the conditions described above.