This is what happens when you open the filters menu on that page. I did not modify anything before taking the screenshot. The page thinks it is already sorted descending despite the URL showing that it is clearly not.
I see the same thing (Chrome, Windows) but can get around it by selecting “Ascending” in the filter box, and then, without closing the box, immediately clicking Descending. Then it re-sorts and modifies the search URL for me. It still doesn’t seem like it’s behaving correctly but I don’t have to manually modify the search URL, at least.
For me, it is possible to change the filter without editing the url. (This is using Firefox 111.0).
Starting from https://www.inaturalist.org/observations/identify, if I change the sort to Ascending and then close and reopen the dialog, it actually shows Descending - even though the url still includes order=asc. However, if I change the filter to Ascending and then back to Descending, the filtering updates as expected (i.e. order=asc is removed from the url).
So, for me, the bug is that the sort filter (as shown in the dialog) doesn’t “stick” on the first try and needs two changes to get it back in sync.