Welcome to OpenStreetMap and thanks for updating this.

Although adding bicycle=no etc. to footpaths tagged as highway=footway doesn't do any harm, it also doesn't really have any effect on routing software which uses OSM data. The implied access restrictions for a footway already exclude all other transport modes. If people are cycling on these paths, they probably haven't been sent that way as a result of access tagging in OSM.

There are times when it can be worth adding bicycle=no, particularly when this is made explicit by a sign. In this case you can also add bicycle:signed=yes (this is what the StreetComplete app does).

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