You have the right to the numerical results (with units and reference range) of your tests. I’d ask for them from both tests. Great news on the hba1c going in the right direction though.
The accuracy of the app predictions is based upon how often you test and how good a representative sample that is. If you always test at your lowest points and miss highs it will predict a result too low. If you test only at the high points and miss the more stable lower ones it’ll predict too high. With finger prick tests there is a distinct risk GIGO applies (garbage in garbage out) when it comes to estimating hba1c. So based on that I see no obvious reason to buy a new meter.
Do you know how many carbs you eat a day/meal? What sort of difference are you seeing between pre and post meal readings? At an hba1c of 64 it suggests that carbs in V ability to cope with them for whatever reason hasn’t been reached. Fundamentally either you don’t have enough insulin to cope with that level of carbs due to low production or you are too insulin resistant for your adequate/ample insulin to overcome the resistance at that level. It makes a difference which, in order to choose the available paths forward for meal and medication choices. It’s also worth noting that eating very low carb and taking sglt2 medication is contraindicated, due to the risk of euglycemic DKA. If they are recommended again please make the prescriber aware you are already eating low carb /keto (whatever is appropriate).