They are using brave search results, like they do with others. Frankly, you could build totally identical arguments (and to be honest, much more serious) for "partnering" with Google and Microsoft, but then the product wouldn't exist and wouldn't be as good.
The relationship with the Brave founder is so indirect, that this - to me - feels like an argument from someone who is looking for reasons to get angry. Kagi probably uses AWS (or other clouds), which funds Amazon (known for terrible worker rights), funds Google, fossil fuel industry, etc. It's a sad reality, but you simply can't exist nowadays in the moral and ethical way many people would like. You can, only if you are a privileged one. Technologically speaking, Google can probably do it, for example (own hardware, DCs, tech etc.). We can choose to fight those that directly support political agendas we disagree with, or we can damage the smallest players by demanding they will be 100% pure and ethical by not having any relationship with those with those agendas.
In my personal opinion, such unrealistic ethical requirements end up being a reactionary choice as they will ultimately impede new - better - players to emerge and will leave the existing - worse - dominating.
This statement makes no sense. Federated search means nothing. Ultimately someone needs to scrape, index, store and retrieve data. At the moment, a handful can do it efficiently, and to have a wide coverage, engines use also other APIs. Kagi does this, for example, by combining Google and others (e.g. brave) with their own indexer.
How do you imagine a "federated" search would be any different? Using multiple APIs is effectively "federating".
As I said in another comment, to be fully ethical you should not run on any major cloud (owned by Amazon, Google, Microsoft, Oracle and IBM), not run on anything on fossil fuels (few DCs), not use any API of major companies (google, apple, etc.) and so on. So basically if we ever want a new, better, solution (tech) we just need to materialize a few billions of dollars to allow this fully ethical solution with no dependency on immoral parties. Alternatively, the whole market dynamic should be disrupted, because that's the problem.