request needs to redirect from https://www.example.com to https://example.com/xyz

If www.example.com and example.com are the same VS, then this is the source of your looped redirect. You hit the same host again (example.com) and then redirect because your HOST ends with example.com...

You need to check the the URI is NOT /xyz already...

e.g

when HTTP_REQUEST {
  if {  ([HTTP::uri] begins_with "/xyz") } {
    return
  }
  if {[string tolower [HTTP::host]] ends_with "example.com" }  {
         HTTP::redirect "https://example.com/xyz"
  }
}

Change begins_with to equals depending on what the rest of the content looks like...