I have yet to complete the Looming in the Shadows special research, and have just acquired the Super Rocket Radar to give you access to Giovanni. When this research was first introduced, the Shadow Pokemon you were given a chance to catch after the battle was Articuno.
New Special Research quest were given monthly afterwards before COVID-19 lockdowns. The Shadow Pokemon at the end of each of these battles changed to a different legendary (Zapdos, Moltres, Raikou, Entei in that order).
With the current Go Fest Battle Challenge, Giovanni's Shadow Pokemon reward is Suicune. I have already caught it from the Go Fest's Super Rocket Radar.
I have heard that Giovanni's legendary Shadow Pokemon changes based on the month, but I am not sure if this is specifically because of the month, or because of the research quest that rewards the Super Rocket Radar. So I'm asking which of it is these, and if I were to use my Super Rocket Radar from the Looming in the Shadows research, would Giovanni have Articuno or Suicune? Of these two, I would prefer to receive Articuno.