The new layout is like this https://imgur.com/3jyDAM5 — you can see the old, now removed, roundabout just below the new road.
The problem is that I can’t delete the existing junction. I can remove various of the elements, but not the actual roundabout or the road lanes leading up to it.
When you say you can’t delete the junction, do you mean that the editor (probably ID I guess) is stopping you? Are you getting a message saying that it is a member of a larger relation? (This appear at the bottom of the screen in ID).
If that is the issue, you will need to remove the ways you want to delete from the bus route relations they are part of. Then when you have mapped the new junction, add the relevant ways to the bus route relations so that they are continuous again.
I twigged to the “member of a larger relation” thing after a while, but even when I’d removed all of the bus route relations, I couldn’t seem to “select” the roundabout or the lanes leading to/from, so right-clicking didn’t produce a context pop-up menu.
I’m obviously doing something fundamentally ‘wrong’ when trying to edit it, but I can’t figure out what. (I’m not an experienced OSM editor, but I have done a bit.)
I don’t understand why the right-click menu doesn’t pop up. But for one thing, they are connected to https://www.openstreetmap.org/way/525407191 part of a boundary=administrative. iD by default may hide them, making you unable to edit them. You need to enable it on the right inside Map Data first.
I suggest you not to remove the relation to avoiding adding work latter. You can simply Sqaure the roundabout, then move it to the correct shape. You should then split the intersection, since bus doesn’t get routed on all the sections (not splitting a roundabout is a historic practice).
I can’t reproduce the lack of a right click menu. I can select the roundabout and bring up the right click menu. The delete option is greyed out due to the bus route relations, but it is visible. Maybe I have some setting different to you that I have forgotten about.
As Kovoshchiz mentioned, the approach lanes share nodes with an administrative boundary which makes things more complicated (even aside from the question of where the administrative boundary now lies - does it continue to pass through the middle of the “ghost” roundabout, or does it automatically reflect changes in the road layout?)
Perhaps worth trying the JOSM editor rather than ID? It tends to be more flexible and allow the mapper more direct access to the raw data. Of course that also means there is a higher risk of getting things wrong - both route relations and admin boundaries are quite easy to break.