Ah that makes sense. The staff being emblematic of the Valar's trust in Gandalf and his authority. It had just seemed like he needed it (in the movies, so maybe not canon) to push Saruman out of Theoden.

So, when Gandalf became Gandalf, his power to affect things was explicitly limited.

I thought it was just that they promised not to use more than a small fraction of their power to influence men, and then only to guide them and not to rule. I had thought the implication was that Gandalf was perfectly fine with using his full power as long as he was opposing a dire threat beyond mortals and could match it's power. Like how he went toe-to-toe with the Balrog of Moria: a corrupted Maiar itself. And that Saruman was effectively using all the power he had as a Maiar to corrupt, mutate, influence, and rule. Explicitly against what he promised to do as an istari.