I wonder if it was just Peter not shutting up that made the spell go weird or if that specific moment is tied into the sudden existence of the multiverse?
Good question.
On another note, I think Strange no longer having his Infinity Stone might be why he would not be aware that the multiverse now exists until it is too late. Or will that turn into an actual MCU plot hole? If the multiverse came into being all along the timeline at the same time, people like Strange should know about it, without realizing he did not know about it before that.
I don't think there's a plot hole in evidence.
The implication of Loki is that Infinity Stones are local - they don't have powers outside their own timeline. So, there's not a strong argument that the Time Stone would inform him about multiversal reality.
And, while he's Sorcerer Supreme, it isn't like he's been studying for it since he was a child, or something - it is a job he's picked up in the last few years, and it may just be a subject that he knows little about.
And also, it looks to me mostly like Strange expects that, done properly, the spell would work just fine. One of his hallmarks is more than a bit of arrogance, after all.