Thibaultmol Thanks a ton for responding to my concern. For a while, I was wondering if I was shadowbanned on these forums or something because this was ignored a couple of times. I even considered emailing support with this question but then I would end up tying my kagi.com user to the username on these forums.
Unfortunately, if what you say is true, then that means there is no help in this area when you use these agents via Kagi instead of going to them directly or via some other service which offers you a similar way of accessing multiple agents. I was hoping that Kagi's contracts with these services offered some guarantees but that not being so is a huge disappointment. In general, I'd be wary anyway but given that I come to Kagi for privacy, naturally the expectations are higher - thus the disappointment greater.
This puts one in a difficult spot: Not having the custom instructions for the Assistant severely degrades the quality of output. Having the custom instructions leaves one in doubt about whether a profile is being built on the other side of the fence. If I wanted to "check something quickly", I feel more comfortable now going to DuckDuckGo's website for their anonymous AI chat rather than Kagi, the service I pay for.
Is my expectation, that I should be able to use the Assistant without a profile being created on the other side, an unreasonable one given that the way Kagi explicitly distinguishes itself from others by promising privacy and minimal data collection?