Thanks for reaching out to Ask Lafeber.
If the toe was bleeding, it’s best to wait until the toe is completely healed before placing him back into a cage. If he reinjures it by climbing, then the healing process may have to start over again. If he’s holding his foot up and not bearing weight on it, you might want to ask your vet if he’s a good candidate for some anti-inflammatory meds to help keep him comfortable during the healing process. Also keep a very close eye on him so he doesn’t start chewing on it. Birds are notorious for picking or chewing at a wound if it’s painful. If you notice he’s picking it, you should call your vet right away so he can find a way to bandage it so it can heal. Often times a bandage made of vet wrap can be used and have a few streamers coming from it, so the bird chews on the streamers and not the toe itself. It’s also important to keep him on a plain newspaper or paper towel on the bottom of his carrier, so his environment can stay as clean as possible.
I’ve had birds with injured toes, and they can be frustrating because they can be slow to heal. If I can further assist you, please reach out.