Some very interesting recent advice from the Scottish Parliament Information Centre on Pavement cycling.
This confirms what was previously suspected to be true, in that a fine can't be given for riding responsibility on the pavement when a route is a core path (which many in the city centre are). Obviously you shouldn't do it everywhere, but it clears up whether cycling in permitted on Rose Street, for example.
Similar advice on legal status of e-bikes.
https://spice-spotlight.scot/2024/07/15/ev-rider/