Unfortunately, before being concerned about carbon footprint, the product needs to come first. I have no idea how an actually good search engine can be profitable and sustainable without ads and tracking, but it doesn't do any good to have a lower carbon footprint than your competitor if you're dead in ten years.
Surely eventually, something will happen. Someone will have a breakthrough moment. As of now, all that's happening in my view is that Google is getting so much worse that it just lowers the expectations for competitors. Maybe eventually it will get so bad that you may as well never use it, but that's not exactly a fantastic outcome.
Is building a good search engine and index from scratch in 2023 simply infeasible? I know Google went through great pains to optimize their index and had a couple novel tricks for ranking results... but the internet is infinitely more massive in every dimension, despite the death of literally libraries of useful blogs, forums and topic-specific websites, and now it seems even Google, with their massive budget, is struggling to deal with SPAM on top of ruining the search experience in general. It's easy to just blame enshittification, because duh, but I wonder if more specifically, the Internet is literally just collapsing under the weight of its own growth and an increasingly weak signal to noise ratio.