The visibility (from __ attribute __(visibility("...")) and -fvisibility) of a symbol can be known from a so file
nm -C lib.so
t is hidden, T is exported(i.e. default). But how to get this information from an object file directly?
nm -C lib.o
Will always print T for non C-static symbols whatever the visibility is.
The visibility is different from whether the symbol is local or global (which is what the lower-case/upper-case letters describe). A hidden symbol still can have external linkage, i.e. it is not limited to a translation unit.
I don't think nm has an option to show visibility, but you can use either
objdump -Ct lib.o
which will show an attribute .hidden if the symbol is hidden or
readelf -s lib.o
which has a column for the visibility (DEFAULT/HIDDEN).