You can use the select-expression in jq to do what you intend to achieve, something as,

jq '.result 
  | select(.property_history != null) 
  | .property_history 
  | map(select(.event_name == "Sold"))[0].date'

Building on your approach, you could, for example, simply write:

jq '[.events[]|.severity|contains("WARNING")] | any'

Or more succinctly:

jq 'any(.events[].severity; contains("WARNING"))' 

If you want to test for the condition in ANY object, no matter where it is, then consider using walk/1.

not should negate the boolean value used by select, so it has to be a part of its argument (i.e. go inside of it):

jq '.[] | select(.email | test("@xyz.com") | not) | {id, username}'

Note: For a simple substring match you can also use contains instead of test, which is used for full regex matches.