I reported this first in October 2021, but apparently nothing has been done. If you re-order tabs (by long-press and then drag), the tab DOES move. The problem is that as soon as you open another tab, the one you moved snaps back to its original position. This is NOT how it used to work and is extremely unfriendly.
Using an iPad Pro 11 inch with iPad OS 16.5.1 (c), though this has obviously been happening for some time. This appears to be a regression.