tolkiens legendarium - Was Gandalf's fight against Balrog a violation of "Inspire but don't fight instead of Men" rule?

As was discussed previously, it is known that Istari were meant to inspire and guide the mortals of Middle Earth in the fight against Sauron.

Does the fight against Balrog in Moria violate that "rule"/"guideline"?

If so, why did Eru restore Gandalf back to life after?

If not, is there a canon confirmation that it was NOT against the rules (aside from circumstantial evidence I noted, namely that Gandalf was restored, promoted and given seemingly greater powers; instead of being punished/demoted)?

I'm guessing it was within the rules since Balrog was a servant of Melkor, not Sauron; and Istari's limitations were on fighting Sauron directly, but at the moment it's a guess not backed up by canon sources.

Answer

No, but not directly because of the power of the Balrog but rather because of the threat the Balrog posed to the successful destruction of the Ring.

In Letter 156, Tolkien wrote about Gandalf:

For in his condition it was for him a sacrifice to perish on the Bridge in defence of his companions, less perhaps than for a mortal Man or Hobbit, since he had a far greater inner power than they; but also more, since it was a humbling and abnegation of himself in conformity to 'the Rules': for all he could know at that moment he was the only person who could direct the resistance to Sauron successfully, and all his mission was vain. He was handing over to the Authority that ordained the Rules, and giving up personal hope of success.

Gandalf's ultimate mission was the resistance of Sauron. In this particular case, the only option for Gandalf to ensure there was any hope of resisting Sauron was to not allow the Ring to fall into his hands, or that of other evil beings. And so he sacrificed his life to ensure that was not the case.

The term 'sacrifice' is key here, I feel. If Gandalf had merely defeated the Balrog without dying himself, it meant that Gandalf had exerted his own power unnecessarily and/or excessively and so be viewed as his failure. But because Gandalf and the Balrog were evenly matched, it was by definition a foe that only Gandalf could face and a threat to the Fellowship that he was willing to sacrifice himself to, so that the mission and the overall quest to defeat Sauron could go on. Even though, as Tolkien points out, Gandalf could very well have believed that only he could have ensured Sauron's defeat and used that as a justification for not facing the Balrog and instead escaping his fate.