Go to Object Mode and run this code in the Scripting workspace:

from bpy import context as C

# you might want to disable modifiers before evaluating this depsgraph
dg = C.evaluated_depsgraph_get()

# deselect faces and edges
for fe in C.object.data.polygons[:] + C.object.data.edges[:]:
    fe.select = False
    
for v in C.object.data.vertices:
    co = v.co + v.normal * 0.0001
    
    # https://docs.blender.org/api/current/bpy.types.Scene.html#bpy.types.Scene.ray_cast
    ray_data = C.scene.ray_cast(dg, co, v.normal)
    
    # unpack; underscored variables aren't used
    result, _location, normal, _index, _object, _matrix = ray_data
    # alternatives:
    # result, _, normal, _, _, _ = ray_data
    # or 
    # result = ray_data[0], normal = ray_data[2]

    # positive dot product says the angle between directions is less than 180d
    is_hit_from_inside = v.normal @ normal > 0
    v.select = result and is_hit_from_inside

You can codegolf this code into a macro:

exec('d=C.evaluated_depsgraph_get()\nm=C.object.data\nfor i in m.polygons[:]+m.edges[:]:i.select=0\nfor v in m.vertices:v.select=(r:=C.scene.ray_cast(d,v.co+(n:=v.normal)*0.0001,n))[0]and n@r[2]>0');C.area.type='VIEW_3D'

[I used inline code formatting so it's easier to select]

You can now hit ⬆ ShiftF4, paste the macro (or type a macro hotstring or whatever), ↩ Enter and it will return to the viewport with the vertices selected. Again you need to be in Object Mode.

Same raycast principle could be used in geonodes: https://blender.stackexchange.com/a/302336/60486

Go to Object Mode and run this code in the Scripting workspace:

from bpy import context as C

# you might want to disable modifiers before evaluating this depsgraph
dg = C.evaluated_depsgraph_get()

# deselect faces and edges
for fe in C.object.data.polygons[:] + C.object.data.edges[:]:
    fe.select = False
    
for v in C.object.data.vertices:
    co = v.co + v.normal * 0.0001
    
    # https://docs.blender.org/api/current/bpy.types.Scene.html#bpy.types.Scene.ray_cast
    ray_data = C.scene.ray_cast(dg, co, v.normal)
    
    # unpack; underscored variables aren't used
    result, _location, normal, _index, _object, _matrix = ray_data
    # alternatives:
    # result, _, normal, _, _, _ = ray_data
    # or 
    # result = ray_data[0], normal = ray_data[2]

    # positive dot product says the angle between directions is less than 180d
    is_hit_from_inside = v.normal @ normal > 0
    v.select = result and is_hit_from_inside

You can codegolf this code into a macro:

exec('d=C.evaluated_depsgraph_get()\nm=C.object.data\nfor i in m.polygons[:]+m.edges[:]:i.select=0\nfor v in m.vertices:v.select=(r:=C.scene.ray_cast(d,v.co+(n:=v.normal)*0.0001,n))[0]and n@r[2]>0');C.area.type='VIEW_3D'

[I used inline code formatting so it's easier to select]

You can now hit ⬆ ShiftF4, paste the macro (or type a macro hotstring or whatever), ↩ Enter and it will return to the viewport with the vertices selected. Again you need to be in Object Mode.

After opening the file, press the "Play" ▶ button, then enter edit mode and you should see some edges have gradients because not visible vertices are selected. Pressing ⎇ AltZ should reveal those vertices.

Same raycast principle could be used in geonodes: https://blender.stackexchange.com/a/302336/60486