Hi there and welcome to the forums!
I'm sorry you are having problems with your budgie. You have been given great advice for your current situation and if you take the time in putting into practice all the research you have made into this subject, chances are high you will be successful in terms of making progress with your budgie.
For now, it would be best to treat your budgie as if you are new to each other.
It's important to just spend some quality time by sitting close to the cage and to work in truly making a connection with your budgie.
This is done by using your voice in a calm, reassuring, positive and encouraging way.
When approaching your budgie, it's important to leave all the negativity and frustrations aside, to envelop yourself with positivity and love.
This may sound strange, but it actually does wonders in terms of connecting with a pet bird and establishing the foundations of trust.
It's also very important to know how to read a pet bird's body language and to only take a more hands-on approach to training when the bird is showing signs of receptiveness.
Another aspect that should be taken in consideration is your budgie's personality. Depending on personality, the time required for a pet bird to be comfortable around the owner will also vary, some budgies take longer in being receptive to training when compared others.
As long as a daily routine is established in terms of training and the bird's safe boundaries are respected in the bonding and training process, then progress will be achieved in time.
It would also be good if you could work on scheduling the amount of out of cage time your budgie has and also establish a routine for when it's required for your budgie to be on the cage, since this is ultimately the safest place for him to be, especially when no one is home.
You can use one of your budgie's favourite perches to encourage him to step up on it. Then you can very slowly and gently lead the perch back into the cage and your budgie will be safely back in the cage.
You can review the info on these links which may be helpful in your journey:
Good luck with everything.