Is it possible to give a budgie too much attention?

That's a good thing, nibbles are good

Where did you get it? It must have been hand fed! What did it cost? In as much as it has snagged your heart, you have snagged its heart as well. Does it know your hand feeds it? Practice a simple whistle all the time. Not a lot at a time but 3 times a day, maybe. That way, if it ever gets out of the house, it will be lost, but will be able to come back to your whistle.
The answer to your question lies in your other responsibilities. It does not need undivided attention at all, for more than a few minutes

you are his mate and constant companion now there is no such thing as too much attention foe a bird , if he gets tired of the attention he will fly off you and perch somewhere high nearby to keep an eye on you

not really, you bonded to your bird quickly. enjoy.

I don't think you can give too much attention especially if its a lone budgie as they are flock animals and you will now be his flock. Its advisable to take it slowly over the first week or so though , maybe five minutes and then s half an hour break in between unyill hes really tame. I talk to my budgies every time I walk past the cage. Finger trained one in the first day and the second in the second day. They are very intelligent and learn quickly. X

As long as that attention does not induce any stress, fear, or injury, it is very hard to over interact,
with most birds.
Sounds like you are bonding well with your budgie and doing it right.
The nibbling and love bites are rather normal for many.
I had one budgie much the same that spent hours after school perching on me or otherwise socializing, like it couldn't get enough attention. I open it cage, and not long it comes to me, perches on my shoulder, pulls and preens at my hair and even nibbles ears.
If your bird is biting at your hand, try giving it a little millet, it may be trying to say I want a treat.

it's hard to give a bird too much attention. since he's so friendly and trusting i'm guessing he's still a baby. he's probably biting because he wants something from you (he's seeing you as a parental figure right now) or he's testing your boundaries to see what exactly you'll allow him to do. next time he bites hard enough to hurt at all blow swiftly for a second on his cere and he should stop right away. otherwise you can try wobbling your hand a little to make him lose balance. he'll stop worrying about biting and he'll focus on regaining his balance