Question about Xiaomi Smart Band 10

Yes, the device logs total daily calorie consumption including estimated basal metabolic rate (BMR). According to the manufacturer, the device displays daily calories and vitality metrics and estimates calories throughout the day as well as during training phases.
Supplementary: The calorie calculation is based on heart rate and movement data (acceleration sensor, etc.), which is why values are estimates and may depend on settings, sensor quality and activity data.