z64 you're right if we think only logically. But I'm surprised now (and I think lots of users will be surprised later) to see the Control Center as something that can change in a non-predictable way.
Until now, my mental representation of Control Center is: a subset of Kagi settings, that are presented to me directly "inside the search I'm doing", for practicality (theme), debugging (status) or user involvement (extension).
It is a static Kagi settings subset, like a handpicked set of common options.
If you think that this will change, I think also that should be evident for the user, something like "Web Control Center" and "Images Control Center"; but sincerely I don't want to manage two different subsets.
So I don't agree with this solution; I'd rather prefer the current status.