The Ancient One said specifically that the infinity stones "create what you experience as the flow of time." And said that if you remove one stone, that flow splits. Banner proposed returning the stone at the point it was taken so it was never gone, thus avoiding the split.
That's slightly confusing, because if the infinity stones create the flow of time, how can it still be experienced if one is removed and not brought back? But it makes sense that if you came from the future, took one stone away, and didn't bring it back, you would necessarily have created two timelines. From the TVA point of view, that would presumably create a Nexus event.
Regarding dimensions, in Doctor Strange, the Mirror Dimension presumably does share the real world's timeline because it is inherently connected to it. But it's stated that Dormammu "dwells in the Dark Dimension, beyond time". Can't have a timeline if you're outside time. (Doctor Strange brings time from his dimension to the Dark Dimension in order to use that to trap him and Dormammu in the time loop, using the Eye of Agamotto/time stone.)
So that implies that if you have a branch in time and two unique timelines, it would be different Mirror Dimensions for each, but still be just the one Dark Dimension for both timelines, because that's outside time and hence outside the split. And the TVA can't represent the timeline for the Dark Dimension, because it doesn't have one.
But there's still a distinction there between the Dark Dimension and the TVA's home (for example), in that Doctor Strange was able to use the Eye of Agamotto/time stone in the Dark Dimension, but infinity stones don't work in the TVA's base, which implies a connection between the Dark Dimension and the reality Doctor Strange traveled from that doesn't apply to the home of the TVA, which could be a unique connection (it's a unique Dark Dimension for that timeline), or not (the infinity stones from any unique timeline might work in the one and only Dark Dimension).
So maybe it's one multiverse, potentially containing multiple unique timelines but currently (from our POV) constrained to one by the TVA, and also containing an infinity of other universe/dimensions, which may or may not be independent of said timeline(s).
But in conclusion, I don't know.