It was assumed that his contract ended after 2023. However, teams are under no obligation to announce extension or terms of FO people. For all we know they already did an extension or are simply planning to do one this offseason while upgrading his title.
And really…I think the assumption might have been wrong. Why would the Brewers having Stearn’s and Arnold have expiring contracts after the same season. That would be pretty dumb. Arnold has always been groomed to take over for Stearns, even Attanasio was pretty clear about that.