Etherpad widget not synchronised

Riot 1:
- Created a room with two admins, (one user on matrix.org, the other on another HS)
- Added an Etherpad widget to the room using the non-matrix.org account

Riot 2:
- Logged in with the matrix.org account in an incognito window
- Switched to the same room to find the Etherpad widget visible but seemingly pointing to a different Etherpad (confirmed by seeing the default text from the non-matrix.org account without edits made from the other Riot)

Riot 1:
- Switched away and back to the room
- Notice that the Etherpads are now the same Etherpads

Reproduce the two-Riot scenario described in the issue: create a room with admins on matrix.org and another homeserver, add an Etherpad widget, and compare it from both sessions. Investigate why the sessions initially resolve different Etherpads; done means both users see the same pad and edits synchronize without switching away from the room.

Written by the indexing model from the issue text.