There are many ways and recommendations on diet and diet change. So all I can offer is my experience and what has worked fir me and multiple species and parrots that came to me on all seed diets. Mine all now eat a huge variety of veggies, leafy greens, cooked safe legumes, quinoa, cooked lentils, variety of pellets ect. They are pretty thrilled now to explore new foods. I'm sure as my flock grew watching each other helped. But they can learn from you too.
First I don't limit their quality seed mix. I offer new stuff spread out in a shallow dish or plate on top of their Cage. I let them explore it on their own. I offer some stuff cooked or steamed, raw, whole, in chunks, or diced and minced. I switch it up. Me personally not a fan of pre made minced chop goop. But many have great success with that. Anything I'm eating or making for myself that is parrot safe they get to.
I did start by offering things by hand to the new arrivals, never chasing them with the offering, I hold up they can come investigate and touch or not, then I leave it for them. Taking a bite first and offering helps too. I usually start with offering stuff that is a favorite of most parrots, even offering a seed by hand. To get them used to coming over and taking it. Like a tiny piece if Apple, or one corner kernel, a pice of pop corn, a crumb of bread. The more textures and things they will try the better they will get a t trying new things. I still do this. Sometimes I walk by and offer a pellet, or a seed, or piece of broccoli, or pice of pepper, of anything. They can't run to me fast enough to take a nibble if whatever I offer. Even if the silly ones have a whole plate of it in front of them. Burds understand food gifts. I really think it helps them understand all this new stuff is food!
Each different pellet is in its own dish. Now a days they only have seeds in their cage, as well as pellets always. But they usually only eat seeds in the evening when I put them up. The rest if the day while they are out they y graze in the veggie and leafy greens , and pellet bowls.
They probably eat 35% seeds.. I'm happy with the variety they eat. They are very curious and engaged with food. Even the budgies chow on everything. Different things go in and out of favor with them. I like giving huge hunks of stuff and let them forage on it.
My one quaker Penny took the longest, and is still the pickiest. It took over a year or two for her to eat leafy greens but now she does.
So I say offer a wide selection, in different ways, spread our so they can explore. Expect a lot if waste, and for many things to be rejected over and over, till one day they love it. Share a salad with them, offer tidbits by hand.
I never thought the budgies would eat pellets! They have seed always available. But they do eat pellets and the love veggies so much!!! I never forced our limited. It like abundance feeding lol!
On toys stuff they can chew and destroy, stuff they can pick at or haul around. Try those cage weavers. The yucca chips, bird bagels, toys that you can hide food in. Food is the big motivation or destruction!
For bump on the log rehabilitation, it can take time and that time can be a year...but the more you enrich their life, the more they will slowly respond. Making a hanging perch jungle gym over the cage top. For me I use ceiling hooks and heavy wright fishing one to hang stuff at head level for them when standing on cage top. And I rearrange properly every month. They love to be like monkeys. And I attach millet spray, or treat Stix, or things to shred in different places on the perches, ladders swings. It keeps them busy for hours.
Also target train, and forage with them at first. Burd tricks on you tune has some great forage teaching videos