Please don’t use the logo for just anything related to Nix. It makes it hard to discern between what’s part of the core ecosystem (“official”) and what isn’t. You can use a clearly distinguishable variant of the logo, i.e. one with a altered shape and color.
Searchix is a great idea and all, and my intention is not to put obstacles in your way. Please keep going, we need more people doing cool new things! It’s just that we have a history of inappropriate use of brand identity that has repeatedly lead to confusion. And it’s not like things aren’t confusing enough with all sorts of things having “Nix” in it’s name.
In case you and others want to make it “official”, let’s instead take the opportunity and set an example of how to do it well: you could start by checking with stakeholders of similar projects (search.nixos.org) how to go about it, and then see from there.