This gets cited here weekly, usually second-hand, so it is worth setting out what it does and does not establish.
HbA1c reflects roughly three months of average glycaemia weighted toward the most recent weeks, which is why repeating it at six weeks tells you very little. The improvement on this class comes from two directions — direct glucose-dependent insulin secretion and glucagon suppression, plus the indirect effect of weight loss on insulin sensitivity — and the second continues after the first has plateaued.
Where I think it is weakest: the subgroup findings are the part I trust least — with enough subgroups something is always significant, and these were not all pre-registered.
The bit I cannot resolve on my own is why A1C lags the way it does, and what to look at in the meantime if you want to know sooner. Tell me what I have not thought of.
Note on sourcing:
Figures above are from the primary publication rather than the press summary. If a number here disagrees with one you have, post yours and we will work out which of us is reading a secondary source.