According to the official patch notes for iOS 13.2.2, Apple addressed those issues, as well as a problem that led to iPhones "temporarily" losing cellular service after a call ends.
However, as is often the case with software development, when you fix one bug, a new one always seems to take its place. Despite Apple's previous updates, it seems background apps were still having issues operating properly post-iOS 13.2.2, but of a different nature.
With the next iteration of the mobile OS, 13.2.3, Apple has eliminated a new bug that prevented apps from downloading content while running in the background. We're not sure how prevalent this problem was compared to the background app refresh dilemma (which was widely reported), but it's nice to see Apple take action regardless.
Other tweaks arriving with iOS 13.2.3 include fixes for the built-in search feature (which was not working correctly in Mail, Notes, or Files), and Mail's message fetch functionality. Apple also says it addressed a problem that prevented Messages from displaying photos, links, or other attachments in the "details" view.
Unlisted improvements arriving with iOS 13.2.3 include vague performance boosts, but it's always difficult to quantify those without consistent testing.