Do I just have to wait for the Bergusia Forge to appear randomly to progress the Izanagi quest now? If so how often do the forges change and when can I expect to be able to further my quest now?
The Forges are now just one Director launch item. And yes, that is the only destination you can select for Forges. The Forge you get will be the same Forge all day. At each daily reset (1700 UTC) the Forge that shows up will change.