How can I Set the profile type to be mirrored along an axis for a vertex bevel? Or should I use a mirror modifier?
As an alternative to a mirrored custom bevel..
Non-destructive work on modified curves has always been a bit of a problem in Blender, because constructive modifiers convert curves to meshes.
I wonder whether this kind of workflow might work for you. First of all, in GN, it converts whatever geometry you give it, to curves:
.. and then sweeps the modified geometry with a provided object:
.. which means, whatever objects are used for path and profile can be under modifiers themselves, (including a Mirror) before being used:
.. as the path (above), or the profile, (below):