I honestly can't remember how sleepy Peanut was at that age but being cuddly is very typical of tame baby birds, so I would expect him to seek out attention and be adorable.
And he's definitely adorable, so cute.
It is more tiring to fly with a clip, since they get less lift they have to work harder.
My lovebird will do basically the same thing, play for 30 minutes to an hour then sleep and/or cuddle for 10-30 minutes. She'll nap longer but usually only if I'm napping too, she joins me in the recliner where there is no danger of her being crushed.
But she's also probably considered a senior so I can't really say if that's normal for a baby. Maybe? The harder she plays, the sooner she'll nap, sometimes in 15 minutes if she's really being frantic.
She has been doing that as long as I can remember (but like I said I can't remember clearly how many naps she was taking when younger. I know she would always nap but I couldn't tell you how frequently. It does seem like it was fairly frequently though.)
Hopefully someone with a younger lovie can chime in.
I know my post isn't very helpful given their age difference, sorry.
Just to be on the safe side, has he been seen by an avian vet? Either while with the breeder or since you brought him home a few days ago?