Hi there and
to the forums!
It sounds like despite your efforts, you haven't truly been able to bond with your budgie just yet. I think that you need to focus more on what he wants instead of what you want--if he doesn't want to come out of his cage, why would you force him to do so? Hiding his cage isn't a good option; this makes him feel trapped and stressed out, despite the fact that he trusts you. Trust and bonding are two different things. Trust is the first step in bonding, whereas bonding is the end result.
I think you need to take a step back from trying to make him do things he doesn't want. It's not necessary for him to leave the cage, so if he doesn't do so on his own, you shouldn't force him. Spend time with him sitting by his cage and talking to him, and don't try to pet him or pick him up against his will. Being attentive to his wants and needs is going to help him come out of his shell more.
Some budgies don't really know how to play with toys. Does he have a bell? A swing? Most budgies love these. Your job is to show him how to play with his things, you can take a toy out and make excited noises in front of him while moving it around, etc. The important thing is to do everything at his pace, and not force him to do things.
He may never be a loud or active bird, as all budgies have different personalities, but it's important that you do your best to help him come out of his shell.
If he seems happy just how he is, then that's great! But if after doing all the things above for a long time, he doesn't seem happy (i.e doesn't move around much, seems bored) then you might want to consider getting him a budgie friend, if you have the space, can afford it, and are ready to take on another set of vet bills. Not all budgies are suited to being solo birds, and sometimes they need a little friend to help them come out of their shell.
If you do decide to get him a little friend in the future, please be sure to quarantine the new bird, which means housing the new bird in a separate cage and room for at least 40 days to prevent the spread of illnesses.
Here's some helpful links:
Meanwhile, you've come to a great place to learn even more about budgies
Be sure to look through the forum's many Budgie Articles and "stickies", which will ensure you're up to date on all the best practices for budgie care.
If you have any questions after reading through everything, be sure to ask!
We look forward to seeing more of you around the forums!
Keep us posted on how your little one is doing, we'd love to meet him when you get a chance!