@Graham_LRR it is literally not part of the underground, in much the same way that the long island railroad is not part of the New York subway. It’s part of the regular train network, aka network rail, just like Thameslink.
Why does it have the same branding? Because it’s run by TfL, who also run the overground, which is also not part of the underground, but which also uses the roundels.
It interchanges with some tube stations, but it also there’s loads of stations on the Elizabeth line that are well outside of underground territory. Lots of regular network rail stations also interchange with the tube.
There are technical reasons as well - tube trains all run on fourth rail 660V DC power, Liz line is 25kV overhead wires - but mostly, it’s a different service with different trains and different drivers.