Thanks for the comments so far
The tubing is Tange Prestige ! Indeed there lugs and it must be brazed. So I would need to check if TIG is possible at all... thanks for the tip ! And maybe add a sleeve because it's past butting (metal too thin).
I would practice before doing this, yeah for sure. This is has been my daily ride for years now, there's no way I'll practice on it.

I guess my question is more of a physics question : if I were to add a tube to make the bike more stable with rear rack loads, what would that tube be ? double top tube maybe ? like Mexican/3rd world type bikes ?

Thanks for the comments :-D