I use Assistant with Web Access on almost all the time as it works best for me. Thus when I turn Web Access off, I typically want this to only be for the current thread. Currently however the Web Access state is preserved for new threads, meaning if I make a new thread without remembering to toggle Web Access I don't get the results I desire, and have to regenerate the response (costing Kagi money).
Sure I should probably pay attention more, but it would be nice to add an option for a default Web Access state. New threads will, well, default to this state, no matter what the previously used thread was set to. There should be three states, "last used" (how it is currently), "Web Access on", and "Web Access off".