How to track brand vs. non-brand traffic

Hi everyone

The organic traffic I get to my site consists of branded searches (eg. the product or company name) and non-branded searches (eg a question or "best xxxxxx in the market"). But I have a problem with:

  1. Finding out how much branded vs. non-branded traffic i get. (Google Search Console doesn't give me the correct numbers)
  2. Finding out the conversion rate for both branded and non-branded traffic, because I can't see the search queries in GA (only some, but most is "not set")

Note: most of the organic traffic lands on the same pages - so I can't say like "everyone landing on this URL is branded, and everyone on this URL is non-branded",

Does anyone know how I can solve my problems?