Hard to see from those pictures.
It is very hard to treat permanently once a bird has it (so it tends to be more of a maintenance thing once it sets in...unless you catch it SUPER early).
Do you have smooth dowel perches and not other types in there? I should rephrase that-- does your bird spend most of its time (sleeping or hanging out) on a dowel perch?
You will very likely need an antibiotic if it is bumble-foot (which means you will need an avian vet)--- and you will need to keep the cage very clean (using an AVIAN-SAFE cleaner, such as F10 SC-- diluted to at least a 1:250 ppm solution---allow to dry before bird contacts it with skin/beak).
The bars on that cage look galvanized..it is possible that your bird is also dealing with underlying issues which made it more susceptible to other issues-- galvanized metals are toxic due to high levels of zinc---they can poison parrots (even though chickens generally do alright with the type of wire).
My Common Mynah started to get bumblefoot and I've been able to improve and stop it. Her vet check last year she didn't need any treatment for it. As said above get a lot of differently sized and textured perches and keep them clean. I also got a flat perch she can stand on. I covered some in vet wrap so they weren't too rough.
I also changed her diet slightly, but this wouldn't be appropriate for your budgie because I needed to add more protein because of her species.
His feet stopped working properly about two weeks ago. I cannot afford to go to the vet and I am trying to treat him from home. I’ll post more pictures to help diagnosis...
I Googled Bumblefoot and this is what I found.
Bumblefoot is a condition that affects a bird's feet, and can be caused by inappropriate perches or poor nutrition. This is an inflammatory or degenerative foot condition that can range from redness and swelling to chronic abscesses. The symptoms of bumblefoot may not be initially apparent to some owners.
Inappropriate perches are dowel rod, pvc pipe, or other very smooth and round surfaces; especially that get feces on them. A perch should be of an approved wooden branch that hasn't been treated with chemicals. There are a number of woods that can be used. These perches can be purchased or made by yourself. jh