(Review requested)

Welcome to OpenStreetMap.

You don't actually need to add bicycle=yes to normal roads (highway types primary, secondary, tertiary, unclassified and residential), as the implicit access in OSM is to allow all transport modes. Also, bicycles and pedestrians use highways in the UK by absolute right unless explicitly prohibited (requiring traffic orders and signs).

On highway=trunk roads it shouldn't be necessary to add bicycle=yes + foot=yes, but sometimes it's needed because some broken routers assume that all trunk roads are high speed motorway-style infrastructure.

The  usual tagging for a public bridleway is horse=designated + bicycle=designated + foot=designated

For the private track, you probably want access=private. There is also ownership=private for unadopted roads which are not gated.

https://wiki.openstreetmap.org/wiki/OSM_tags_for_routing/Access_restrictions#United_Kingdom