Avengers: Infinity War, Doctor Strange uses the Time Stone to predict the exact chain of events, including his own temporary death, that will lead to ultimate victory against Thanos. Naturally, he does not tell Iron Man that his death is a necessary step along the path to victory. When the time comes, Iron Man is willing to make that sacrifice at just a nod from Strange, and the faith in Strange's implication that it was the exact chain of events the sorcerer had foreseen for victory to take place.
All of this, including Strange's direct involvement in Iron Man's death, will be something that he has to deal with in Multiverse of Madness. While survivor's guilt has been explored before, Doctor Strange didn't directly fight Thanos in Infinity War and knew from the outset that his actions would lead to Iron Man dying after starting a family. To have this kind of knowledge and to make that choice for Iron Man would impact Strange emotionally, especially if the explorations into the multiverse show him what the world would be like had he chosen otherwise. Multiverse of Madness, therefore, gives one of the most concrete opportunities for an MCU hero to have certain knowledge of the consequences of their actions.
Doctor Strange's journey of character development has had his own ego be one of the largest impediments to his growth. Starting out as an arrogant but gifted surgeon, he was briefly humbled by his accident - but then found new status as a gifted student of sorcery. With the Time Stone lost, Doctor Strange's power is diminished, but as this is an external facet of his abilities - an unquestionably useful tool, but a tool nonetheless - it is unlikely to affect his self-regard. However, being faced with the consequences of his actions, both by reflecting on his short-lived relationship with Iron Man and possibly facing the man himself in another dimension, might force Strange to confront his own choices that led to Iron Man's death.
Most humbling of all - and potentially the resolution to Strange's emotional journey - would be to encounter a Tony Stark that refuses to allow Strange to take on that burden of guilt entirely. Iron Man was a hero; his loss provoked a strong emotional impact on those that knew him. Iron Man's journey was from being a person who was a loner to being a person who was willing to make the ultimate sacrifice. With Avengers: Age of Ultron, there is a great deal of textual evidence that suggests that while Doctor Strange may have set up the scenario so that Tony's sacrifice could play out, the decision was made by Iron Man years beforehand.
Whether Doctor Strange realizes it or not, his decisions can inform the world around him - but however much power he has, he cannot control everything. Given that the sequel addresses an array of worlds splintering on decision points, Strange will get an unparalleled opportunity to realize this humility; to mourn and to grieve someone that he respected, even if their relationship was tense. Doctor Strange in the Multiverse of Madness will allow Strange to come into his own, and may even teach him the value of being a team player.
