Please don't change highway=footway or highway=cycleway to footway=path. The default access assumptions for footway are unambiguous, those for path are not. Where ways were mapped as cycleways and had access tags (which you should not have removed), this would also break cycle routing.

Unfortunately, the names of some OSM tags are a little unhelpful and counter-intuitive, but for historical reasons we're stuck with them. If it looks like a path, it's probably highway=footway. What the law defines as a footway and everyone in the UK calls a pavement is usually tagged highway=footway + footway=sidewalk.

The mappers who added these features to the map almost certainly chose footpath for a reason.

In my opinion (and other will differ here), the only good use for highway=path is for desire-line paths also tagged with informal=yes, because no access values can safely be inferred in these cases.

I have reversed your changes because it is important that cycle routes are restored before the OSM daily extracts used by routing engines are produced.