Do you have to finish Looming in the Shadows to get the next Team GO Rocket Research?
Solution 1:
Yes, you need to finish Looming in the Shadows to get the next research task, A Challenging Development.
The quests in this series are actually identical. Every month, if you have completed the previous quest, you get the new one. The most important reward from the quest is the ability to fight Giovanni and get a shadow legendary Pokemon. Each quest lets you get one of those Pokemon, and the Pokemon you get depends on what month it is when you do the fight.