If it's in the same ticket, on the way in you need to get your bag and do immigration and customs. Once you're out, you'll have to either walk or take the bus until Azul's terminal. Note you're not airside anymore. Then, you usually just go to the counter and give them the bag. Ask them for new boarding passes since they're different than the ones you got. Next, you do security and you're good.

Sometimes airlines have connection areas outside of customs where you can give your bag but in my experience with United that hasn't happened.

The way back will be easier since you check in your bag all the way and don't need to get it back in GRU. However, you still need to go through international security and often it's a long walk from the domestic terminals to terminal 3. We never took the bus though.

Note that on the way back you need to go to the United agents at the gate to get the correct tickets since, again, they're not the same. The tickets you'll have that look like a receipt with a QR code will give you access to the gate but you'll need the correct US-like tickets to board the plane. Last time I was in line to board and people in the line were furious because they had not done that and weren't allowed in the plane until they talked with the agent at the gate. I'm not sure if you're allowed to check in with the app (I guess not, otherwise those people wouldn't be upset).