It's been a while since there were updates on this project, but here is a new presentation from the City on the proposed pedestrian/cyclist bridge on Richmond, north of Sunningdale.
https://pub-london.escribemeetings.c...umentId=105481
It looks like the detailed design will be finished in February 2024, it does not say when construction would start.
This new bridge would facilitate an "east-west recreational pathway corridor along the northern boundary of the city".
Here is a long-term vision for the pathway. Red is the proposed pathway as part of this project. The green pathway is already constructed, and the yellow lines to the east are potential future pathways when those lands get developed eventually.
When Sunningdale gets widened between Richmond and Wonderland, a new bridge will be built over the Medway Creek which would have an underpass for pedestrians and cyclists, thus connecting the Medway Valley trail south of Sunningdale to the new pathway to the north.