yes we are indeed a standalone, the sizes of bubbles are reflections of the number of index-usage relationships yep is attached to ahrefs: https://techcrunch.com/2022/06/03/yep-search-engine/ where I can speak to where results come from, I couldn’t tell you about their model
there’s a safe mode if it’s of use: nested in the settings gear menu but also on /preferences (to turn it on for all searches)