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But is it the full power of the entire life of millions of suns or the equivalent of what millions of suns produce in a millisecond?

Power is by definition per unit time.

Although these bursts are coming from a place where time is rather more spread out than it is here.

What does that mean!? Might a millisecond there last as long as a few of our Earth seconds? What is this concept called ( for me to read up on it)?

My assumption is that the place that this burst is coming from is near a very large, very dense mass.

That wasn't a joke on units of measurement. It was a joke on grammar.