Adding wheelchair=no alone would have achieved this.

If the surface is grass, as it appears to be, adding surface=grass + tracktype=grade5 would be useful.

It's obviously not informal=yes, as that implies a desire line path, not a planned path in a landscaped garden.

For access tagging the defaults of highway=footway + foot=customers were correct. Setting foot=yes implies a public right of way, which is clearly not the case within the grounds of RHS Wisley.

I cannot see any steps on the aerial imagery and a SAC scale of mountain_hiking (terrain is steep in places and may pose fall hazards) seems improbable.

Please only tag what is actually there and resist the temptation to add fiction in order to influence the behaviour of rendering or routing software.
https://wiki.openstreetmap.org/wiki/Tagging_for_the_renderer