My first assumption is that this is because being vaccinated felt like it was doing something “good” for your health (decreasing depressive symptoms) and decreased anxiety related to fear of catching Covid. It would be interesting to see if it is instead related to occupying the immune system and resulting in less systemic inflammation. I noticed decreased symptoms from my Ulcerative colitis for the months post vaccination, which is a immune system related condition, so I somewhat speculate that my immune system was too preoccupied to attack my gut. Something similar may be happening with anxiety/depression but without more rigorous studies it’s hard to know.