Hi @ahargreaves_FW,
> am I correct in thinking I can only build a WAB from a "classic" web map and not from a web map build and saved in the new "beta map viewer"?
Correct. And it's because the new AGOL Map Viewer was created AFTER ArcGIS Web AppBuilder. The former uses new JS libraries that Web AppBuilder does not have. Sorry.
For web maps created with the new Map Viewer, try using ArcGIS Experience Builder.
Hope this helps,