Pretty cool feature. The unstated downside is that any personalization settings like dark mode, translation, and lens settings are still seemingly tied to account login.
We even considered variations of having some settings preserved in local storage and impact of that on anonymity. Ultimately decided that was not worth it.
Check the FAQ section (towards the end) for full details and analysis:
You could have a few built in options (like for domain filtering and customisation) for the privacy people. Could even be community sourced so there's no onus on Kagi itself.
So for example there could be a built in "developers" preset that might make domains useful to coding higher ranked (and down rank or block things like stack overflow clones). Etc etc.
Basically this could allow a smaller amount of customisation with less ability to identify a specific user.
I also use Orion and I do like the idea someone else had of integrating an option for Kagi Privacy mode into the "incognito" tabs specifically as an option!
Though those still get passed to the server, and your combination of personalization settings is likely to be globally unique, and it's almost certainly unique among the subset of users that are paranoid enough about their privacy not to store preferences in their session... But still.
Not only that but your searches themselves likely give Kagi more than enough information to identify you as an individual. We saw that nearly 20 years ago when AOL searches were published and people were able to track down specific individuals from their search terms. (https://www.nytimes.com/2006/08/09/technology/09aol.html)