I think there are a couple of important items to understand.
HbA1c, CGM, and glucometers measure very different things, and while formulas have been developed to translate values between these tests, they are only estimates. HbA1c measures how many glucose molecules are attached to your red blood cells. As these cells tend to live 3-4 months, it is generally accepted that the glucose concentration here reflects your average glucose levels over that period. Glucometer measures your blood plasma glucose levels - it works a little bit like urine strip, blood reacts with chemicals in the strip, strip changes colour based on the current level of glucose in your blood and then machine reads it and displays a number. CGMs measure glucose level in your interstitial fluid and try to approximate this to your blood plasma glucose levels through an algorythm.
All these devices, whether professional or consumer, come with their own margin of error and testing conditions, which can also affect the outcomes of these tests. Lab tests are generally considered a gold standard, with consumer devices being quite precise but more indicative of your actual blood glucose levels.