Using Outlook for iOS for personal email and calendar management
Hello Lukas,
One thing worth checking is whether Outlook can remove these entries individually. When one of the old searches appears under Recent Searches, swipe left on that search suggestion and delete it. Microsoft documents this as the way to remove individual search-history suggestions in Outlook for iOS.
If that works, it may at least let you remove the old entries individually even though Clear Search History has not cleared them for you.
If the suggestion cannot be deleted, or it disappears and later comes back, I would stop reinstalling Outlook or changing the Google search-history settings since you have already ruled those out on multiple devices. At that point, I would report it through Outlook > Settings > Help & Feedback > Contact Support, mentioning specifically that the Gmail search suggestions persist after clearing the history, reinstalling Outlook, and changing devices.