Which kind of browser are you using? Chrome (branded)?
Which version of the browser are you using? v137.0.x?
Which version Katalon Studio are you using? v10.0? 10.1? 10.2?
If you are using Chrome (branded) v137, then the following issue would concern:
I mean, when Katalon Studio v10.1 and older launches Chrome (branded) 137.x, it will fail to activate Chrome Extensions(due to Chrome’s security policy). Possibly Flurp Extension in the target web page won’t be activated. Therefore Web Recording tool would not find Flup Extension in action in the page.