An inset that resets its font (like Footnote) does not care at all
about enclosing font. Therefore the real starting point is the class
default font. This avoid cases where the footnote contents is forced
to \normalsize.
It turns out that the Greyedout note inset, did inherit font but was
declared as not doing it. This commmit changes the definition by
adding \normalfont\normalsize so that no inheritance happens.
Note that actually \normalfont resets everything but the font size.
This does not matter for footnote (which has its own font size) and
greyedout (which is fixed now), but may matter elsewhere. Also, I do
not know what the situation with HTML is.
0789f2f2ae