I’ve never applied for strictly a UX research position, always UI/UX. For those types of positions people care about the design more than they do about UX although they may say otherwise. But as long as your UX is not clearly terrible then you’ll be judged on design. It’s probably different for strictly UX research positions.

For portfolio, showing the thought process is more important than the number of items in your portfolio. If you redesign something, have a page that goes into detail about what and why and a bit about how.

Also probably can’t hurt to have one or 2 “eye candy” pieces that maximizes the experience. Sometimes those help a lot.

At the end of the day it really depends on what people are looking for - and everyone has different ideas about what the position entails.

I’m happy to give you some portfolio feedback if you need when it’s ready to look at.