The keets (sorry, I have a hard time calling them budgies) have been eating or at least playing with greens for a while now but I couldn't get them to try more solid veggies like celery or broccoli.
Gave them a large chunk of celery last night just to see what happened and they went right at it so today, I took the kabob I have for my conure that he never uses and put some big veggies pieces on it. Seems to be a hit, both are eating broccoli which they wouldn't even try before.
This particular kabob is one made for rabbits, it had wooden toys on it that can be replaced. It was a lot cheaper than reusable kabobs made for birds. I think there was a eve shorter one at the pet store, If there is I'm getting it too.
I'm glad to hear your budgies are starting to enjoy their healthy vegetables now!
Lots of times, the way the foods are presented make a big difference in whether or now our budgies are willing to try them.