what does"recovering" here mean?

It's sarcasm.
You will often hear the term "a recovering alcoholic or drug addict". These are people that fought with addiction and are clean, or drug and alcohol free.
In this case, the author once worked in Public Relations and he either hated it, or it took over his life - too much work, whatever reason he quit it's an inside joke for him, or presumably people that have worked in this industry will get or at least be able to commiserate with.