The UV that you want visible in the Image Editor must also the UV active rendering option enabled for it. The reason I am saying this is because if an active UV that is not UV unwrapped, you will not get any displayed UVs, because there are none, active.
A tip:
In the Text Paint workspace on the 3D Viewport the TAB switches (like in almost all other workspaces too) between the special used default interaction mode and Edit Mode… where you can select all the faces which you want to see the UV’s in the Image Editor in Paint Mode.
So you do not have to switch the workspaces. Something similar works for sculpting when you want to use face sets from selected faces ( Face Sets → Face Set From Edit Mode Selection )… just hit TAB.
It’s just the fastest (and if you think about it straight forwardest ) thing to do to select the faces you want to work with… and also in the context of UV’s.
(Switching UV Sync Selection in UV editor also would do this…)