Anyone else's blood boil at a world historical genius being required to verbally bow and scrape before an adolescent that did nothing more significant that being born to noble parents?
Why do you think he was required to verbally bow and scrape? The sample letters here show nothing more than ornate politeness.
His brilliance was known in his own time and he was respected and established at court.
Whether he saw advantage in this connection for financial, social or purely altruistic reasons is debatable, but it is presumptive I think to declare subservience.
More exploration of the possible context and relationship between them here:
Royalty commanded resources which Euler wanted to access, even if indirectly. In the modern world, geniuses have to do the same to e.g. gain funding. Maybe there is slightly more meritocracy now in determining who gains that level of power, but the improvement is not nearly as dramatic as you'd like to think. Nepotism is alive and well.
