As far as I know there isn’t a currently accepted or widely-used way to tag/map this.
Everyone is free to come up with tags that they feel are appropriate, so you could tag it as something like foot=yes_if_you_crouch
but there would be no support from routers.
You could attempt to approximate it with tags like maxwidth:physical=*
as specified for Tag:barrier=cycle_barrier - OpenStreetMap Wiki. opening=*
as described on that page is another option, but probably less widely understood.
An unorthodox option could be Tag:barrier=height_restrictor - OpenStreetMap Wiki with maxheight=1 m
or so, but I doubt foot and bicycle routers look at maxheight tags, and this barrier isn’t really a height restrictor.
wheelchair=no
and an appropriate wheelchair:description=*
are an option since wheelchair:description is fairly widely used.
Personally I would tag this as barrier=lift_gate
, motor_vehicle=private
(or other value as appropriate), and a human-readable description=*
describing foot/bicycle access possibilities.