Search gives solid options for one week, month, or year, but if you want something outside of that range it gets super annoying to manually type in two dates (often I want something in the six month or less range or the more than a year range). I think we can be easier! My suggestion is to make it easier to select a different look-back period from the current day (a precise range option would still exist). The thought is to make the current options show an ability to increase / decrease the look back period. So, if you click on year, text changes to indicate you are now looking back 1 year, if you click again two years, so the user could quickly click and get, say a 3 year and 6 month look back (or 5 weeks or whatever). My rough tought is, basically, once you click, a visual que that you can increment or decrement show up, but, if you don't make any further changes after a 2-3 seconds it just accepts the range you have. Other thoughts were some sliders, though I think that might get tricky for different screen sizes and probably slows down most users quite a bit.
I think this is pretty straightforward. I looked and Google, Bing, and DDG are close to what Kagi now has.