Using the 13.3 beta, haven't actually gone so far as to do an actual time test on the background process kill time, but it sure as heck is improved and seems to be back to normal.
For instance, if I did a search in Amazon on 13.2 and left the app, even for a couple of seconds, when I returned the app would reload and the search gone.
After installing the 13.3 beta though, I did the same test and well, two days later if I go back into Amazon, the same search results are still there. That's more like it.