Does inhaled corticosteroid treatment (for asthma, specifically breo-ellipta) weaken the immune system further (i possibly have an autoimmune disorder too) and make one prone to infections?

The drug action and metabolism occurs at the level of the lung tissue where it first enters. The amount that progresses into other body tissues is trivial. As such its effect on the immune system is not clinically significant. This is why inhaled steroids were such a great advance over the oral or injected forms used previously that do have an impact on the immune system.