By itself, Adobe Launch (or what is called Adobe Experience Platform (AEP) Tags, nowadays) doesn't really send those network requests. Rather, Launch loads the necessary JavaScript, in this case, the Adobe Analytics' AppMeasurement.js, and that latter code sends the network requests.
I don't know of any client-side method for capturing a user's browser network requests to send somewhere else. Perhaps instead of recording AA's network request, you could record the contents of AA's "s" object, since the "s" object's contents (i.e. the eVars, props, etc) would contain the information that is ultimately reported in AA. You can use https://experienceleague.adobe.com/docs/analytics/implementation/vars/functions/registerposttrackcal...for that.