How can I work better with toxic staff engineers and bring this to my manager's attention?

First, I'm sorry you are going through this. It can't possibly be easy to motivate yourself to go to work every morning.

My initial gut reaction is that you should just leave. You are 8 months into this role, so it's past time I would shrug off the bad behavior you described as "miscommunication" or "unintentional". Removing people in power is quite hard for leadership to do, and requires a lot of explicitly terrible behavior for it actually happen - and it doesn't sound like that's a bridge any of the managers wants to cross.

I am a bit confused by the presence of two staff engineers on the same team - staff engineers generally oversee the work of 10+ people, so I presume there's at least 20+ people in the team. That's a LOT of people on a single team / feature. If not, it seems their titles are inflated - their behavior certainly doesn't indicate they know how to be an effective staff engineer. It simply seem like these two are monopolizing power and not actively sharing it w/ people on the team. In any case, you can elaborate more on the team structure and the operational problems you see, we may be able to help more.

Still, it may still be some time before you can leave. So I would still try to at least find one thing that you can do on your own (that doesn't need anyone's permission) to improve the lives of people around you in the meantime. Maybe you can start documenting all the learnings from your oncalls, eventually making an oncall handbook. What you despite unfavorable situatio will go a long way to boost your own confidence, (doing so did for me).

I'm sorry to hear that you're going through a tough time. However, I feel that I don't have enough context to provide you with specific actions. Moreover, taking any specific action may not help and could potentially lead to another argument with your staff engineers.

During our professional journeys, we may encounter toxic environments. However, it is essential to remember that this is just one small phase in your overall journey. Consider it a learning opportunity. Remember that everyone faces similar problems but handles them differently. Rather than focusing on winning arguments, aim to get the best out of the situation.

Please take a step back and consider the following:

1. Working backward plan: Determine the end result you are looking for and build a plan to work backward from there. Define your role expectations and see how you can meet them within the given environment limitations. Also, Identify the cheerleader for you who can recognize your efforts. Return the favor by help others.
2. Deep dive: Double-check the facts and remove emotional strings. Make a list of things that are in your control and things that are not. Focus on things in your control and see how you can achieve the end result listed in step one above.
3. Earn trust: Learn the rules of the game. I highly recommend finding a middle ground to work with the staff engineer. They have domain knowledge that you should respect. Instead of finding their shortcomings, ask for their opinion and offer help. They should feel that you respect their experience.

I know I am not giving you specific help here but hope you find these points useful.

The staff engineer overseas the work of 1 NCG, 2 contractors and loosely a UI Engineer.

He is staff because of his industrial expertise on the feature we are working on

The contractor ( who works as staff ) overseas about the same ( maybe few more contractors)

I see a lot of areas where I can make an impact to grow into staff in here. But but but …. The environment needs to support it more the code and impact I have.