Is the end goal to ween onto their own index or will the search space always be dominated by some major upstream players?

I'd be surprised if that isn't their eventual goal, but I don't think it's really possible to deliver the kind of general-purpose engine they want with a team of ~5-10. Hopefully if they're successful and grow they can expand their own indexes.

You can try them at https://www.teclis.com/ and https://tinygem.org/.

I guess it depends on how much traction they get, both by consumers and also with websites.

AFAIK some websites actively or passively block everyone except Google.