> "This heightened glycolytic flux leads to higher glucose uptake"
This is a dubious statement. While glycolysis indeed consumes glucose, the amount of that consumption is expected to be significantly lower than through oxidative phosphorylation.
For example, if you deprive cells from oxygen, oxidative phosphorylation gets inhibited and glycolysis kicks in as an alternative metabolic pathway. As a result, blood glucose level goes through the roof. This is what can be seen in patients with acute respiratory distress syndrome.
But it is more complicated than that - when oxygen level drops, the nervous system starts gluconeogenesis as an attempt to compensate for the lack of oxygen by increasing the levels of glucose in the bloodstream. So we have multiple parallel effects going on: lower glucose consumption by oxidative phosphorylation due to the lack of oxygen + higher glucose consumption by glycolysis + higher glucose injection via gluconeogenesis. The net result of that formula is that blood glucose level goes up for almost all patients with hypoxemia.
Still, glycolysis alone cannot explain the effect of metformin. If it was really a glycolysis with such an amplitude caused by metformin intake, people would start to develop lactic acidosis, air hunger, cellular damages, neuropathy, dementia, cancer.
Honestly speaking, the only viable explanation so far is that metformin may cause mitochondria training by mildly and temporary putting a strain on ETC. Like a mild physical activity would do. Anything more impactful than "mild" would lead to an excessive oxidative stress, cellular damages, air hunger, suffocation, and tons of dangerous consequences.
Some papers also claim that metformin inhibits gluconeogenesis thus lowering glucose levels, which is another argument in favor of the "biochemical training by metformin" theory. Mitochondria seem to become more robust after a mild stress environment created by metformin, as if you visited a gym.