Sorry I don't have any answers, I'll post this to "bump" your post to the top of the list to see if the second pass will get you some useful inputs.
That said, I have read many posts about people who have high HR when awaking, not so much otherwise. I don't recall the reasons/discussions, but I know there have been some.
My guess is you may be having dreams that are stimulating your heart rate. Do you have any recollections of dreams when you first awake?
My heart rate lying in bed is usually 60-65 bpm. It is only when I get out of bed and I am standing that it jumps to 120 or higher. I have been having weird dreams lately though.
I have also look at the posts concerning high heart rates in the morning and they all attribute them to anxiety. As I have been dealing with an anxiety disorder for a while, I know the symptoms, and this is not that.
Well the good new is a resting of 60-65, that's agreat HR, suggests to me a strong cardiovascular... but why the higher HR when active, this suggests the opposite.
Metoprolol (any beta blocker) can cause dreams, described as "vivid". I have that problem myself, but I take a much larger dose of BB, 100 mg... and as much as 100 mg twice a day. Still, I am not sure the BB is causing the dreams, even on my part. But, it dreaming started when you went on BB, it is the likely cause. .. an unwanted side-effect.
If just standing pushes you over 100 bpm, I think that is too high. What was the BB prescribed for, high HR, or BP, or both? I understand your HR does settle down after you are up a while. That my be the BB taking effect, if you take it in the morning, that's the usual recommendation as even the Slow Release is stronger in the early hours after ingestion, I think. That should also minimize dream effects.
If you're being treated for a high HR (tachycardia), and the BB is working, I'd not worry a lot about a little rush in the morning, so long as that peaking of HR isn't over 130, my number, not a medical recommendation. Then too, I'm an old guy who thinks he's doing well if I can get my HR below 80 at rest. I don't know what it is when I sleep, for obvious reasons. I have been on a monitor, but didn't ask what the rate was during sleep. With the dreams I have it could be high at times.