Nah AGT and Picard don't happen in the same timeline. AGT was some sort of alternate timeline. But the events of the Prime timeline diverge enough from the AGT timeline that it makes more sense that the new warp scale was unique to the AGT timeline and didn't happen in the Prime.
The TNG Technical Manual explains the change, it went from a cubic function to a logarithmic function along with some technobabble justification for why. There's also some interesting background info and formulas on Memory Alpha, apparently the scale change happened in 2312 according to some magazine.
I forget which episode used it, but there was a graph of the "warp barriers" on one of the ships. Maybe Archer's Enterprise. It's on Google.
Anyway the graph shows the different energy thresholds that must be output when moving between different velocity levels. Presumably every warp level was at least double the previous amount (edit, it's actually exponential!).
The chat can extend beyond warp-10 but there may be a cutoff point where the energy required to push into the next threshold is no longer an effective use of resources.
It's inconsistent. Canonically in most Trek warp 10 asymptotically approaches infinity, which is why you see a lot of nine-point-nine-something when really high speeds come up, but every now and then the writers forget and you'll hear about exceeding warp 10.
You also have things like transwarp, quantum slipstream, or the proto-drive which operate on different principles and don't follow the warp curve. Their equivalent warp factors would just involve stacking up ever more 9s after the decimal point, but their speeds aren't typically expressed in terms of warp.