I also have a morning rise in BGL. I have been getting a bit slack and also had to stop medication (metformin) for a couple of days.
I don't normally monitor my BGL (GP says not normal to do this if not using insulin, instead to rely on HbA1c tests a few times per year) but I decided to check (GPs have all but shut-up shop - due to covid supposedly) but 10.5 to 11.1 both before and after metformin break, is higher than it used to be. With diet control the morning spike used to be around 7 to 9. It drops during the day.
I found fasting BGL in the morning to be sensitive to the amount of sugar and simple carbohydrate eaten in the previous evening. I suspect my liver contributes a basic morning BGL of about 6.5 (say 18 hour fast). In reality I will be happy when I stabilise it again in the region 7 point something. Or when my HbA1c is steady in the NHS OK zone.
The BGLs always seem a bit high even in the day but the HbA1c has been in the OK diabetic range. I don't know why the OK range is so high (up to 59 mmol/mol) if taking metformin, it is well above the non diabetic range. (HbA1c ranges for diabetics using metformin a another topic - I mat ask the community about that, OK level in NHS, NICE guidance:
Pregnancy or diet controlled patients <48 mmol/mol
Tablet treated 48 - 59 mmol/mol
Insulin treated 53 - 59 mmol/mol)