I'll give my two cents on the subject, I’m a 42 Student, and whenever someone searches up something on my laptop, they always go to something along the lines "what's this search engine?" I never really saw anyone confuse it with any existing search engine.
To be fair, search engines are one of our main tools and we do heavy use of them, so 42 Students may be more prone to notice changes in the search engines.
Lastly, I personally think this discussion is somewhat over anyway, it feels too late for Kagi to change it's logo in any way, the branding is definitely set and established at least for a while.
Whether it's in videos, blogs, and even the merch, the current branding is used and changing it will lose a lot of precious brand recognition.
Last lastly, I think the branding is very cohesive and well-thought out, with the background indicating different services...
After updating all my apps, it looks like it doesn't feel cohesive anymore (wasn't assistant a g with a purple background at the start?) that might be something to work on though as individually these are great logo's but they don't have a cohesive look together yet:
