I’ve looked at your YT video and haven’t been able to ID the field yet and have to rush off to work now. I’ll have another look when I get in tonight. To help confirm that you have got JWST I attach an image I took just at the start of your set (Jan 4 at 22:29). The trail of JWST is marked. The upper stage is around 3 magnitudes fainter than JWST and around 2.5 degrees west of it so your other object is not the upper stage. I can probably identify it if you let me have an accurate position.
You can get an accurate ephemeris of both JWST and the upper stage from here:
This is based on amateur astrometry of both objects and is pretty well up to date.