Ha, I was looking for your post as I had a few thoughts.
I am not by any means an expert of course.
So what you are describing, the "feeding" of toys, is not merely "Dad" behavior but also "Wanna-Be-A-Dad," aka COURTING behavior. In budgies this can be simple friendliness or loneliness, or it could be some hormonal behavior.
There are lots of posts around parrotforum with regard to discouraging hormonal behavior, and it applies to budgies as well. The quick version: No Shady Spots (yes, you can cover the cage at night); 10 to 12 hours darkness at night for sleeping; Nothing that can seem like a nest. No hidey-huts nor coconuts etc. IF you pet or snuggle with your little budgie, no touching below the neck. Hm i feel i may have forgotten something, but a quick search for "hormonal" on parrotforum should help.
Personally I would suggest slowing changing up the toys. Adding more toys, and gradually removing this one. (Gradually, ie move it over a bar or two every day or so, as it will become slightly less accessible and then eventually it will disappear...) Make sure there are not any toys with Actual mirrors. (Yeah they might chase reflections in their food bowls or etc, I would not worry about that too much, but no actual mirrors to befriend.)
Changing the toys is mainly for the purpose of removing that attachment, but also it's another anti-hormonal tip. I read elsewhere that our timid little budgies get more hormonal when their enviroment has less-changes, as they feel more secure about building a new family. But, you don't want your budgie to feel UN-safe, so make changes somewhat gradually. But, do keep making them!
Hopefully your budgieboy has a nice spacious cage, and will have space for multiple toys. Right?
You might consider getting him a friend, especially if you are sure he is a boy. You might consider getting him another boy budgie. With many parrots this is not recommended but budgies really are highly social creatures. Yes they MIGHT not get along (in which case you would need to house them in separate cages) - but with budgies there is a good chance they would.
If getting him a friend is not a good option for you, or even if it is, you might also want to try finding some youtube videos of budgies to play for him daily. There are numerous multi-hour videos of people's budgies, basically recorded exactly for the purpose of providing budgie-sounds and sights for lonely singleton budgies. (My Jefferson-budgie Loves these (even though he Does have a missus-budgie as well). In fact I've just recently realized that he believes a couple of the flat-screen budgies belong to His Flock.)
As far as eating lots of food. Well just go with it, make sure you provide him plenty of food. If he is regurging it, then it is not gonna make him fat. Let him have veggies or veggie chop, and a good seedmix that includes good pellets, and / or if he's already on a good pellet diet then keep him on that (with veggies!). If he has plenty of space and he's active, he's really not gonna eat more than his little body needs.
I clip raw veggies all around inside the cage daily for my birds. (Instead of chop. They have beaks! They can chop it themselves!
) They like them as chew-toys as well as for the eating. My budgies' favorites are romaine lettuce leaves, carrots (peeled of course), and broccoli tops. They really like romaine lettuce leaves, & sometimes attack them like little lettuce piranhas. Organic is preferable of course. If not available make sure you wash it really well.
