I've had another wander around this evening (I needed the exercise anyway :) and I think the only section that is explicitly "pedestrians only" is the main path through Botanic Square.

https://ibb.co/n8VK0FV
https://ibb.co/mzCHwBf

Other paths either state "no vehicular access" or don't state anything at all (apart from e-scooters being banned at both the northern and southern end of the estate).

https://ibb.co/t8Jy81M
https://ibb.co/sP5wfr2

I'm not proposing to tag any of these as shared cycle paths, but I also don't think they need the bicycle=dismount tag added explicitly.