In MY MODS, mods that have an update on Thunderstore come first, in every
sort order and with any filter or search. They keep their order among
themselves, and so do the rest.
Only the list changes: the load order, and so which mod wins where two
change the same thing, is as it was.
The arrows that move a mod in the load order are off while an update is
waiting, since the list is not in load order then; the tooltip says so.