There is no direct night train Italy to Barcelona.

There is nothing overnight even vaguely in that direction from Italy.

Milan/Northern Italy → Barcelona is a very long journey, very expensive and complicated to do it in a day (2 x 30€+ mandatory seat reservations).

I’d advise to travel to Toulon, Marseille or Avignon the first day, spend a night there and the next day travel to Barcelona

There is an overnight ferry Genova - Barcelona operated by GNV. No pass holder discount though.

I would check out reviews of the GNV ferry company first. I’ve seen some really bad reviews for another one of their routes to Sardinia. 

Irrespective of quality the cost is very high compared with an overnight stop half way there. You can easily travel  to Marseilles from Milanin a day and then the next morning make your way via Port Bou for connection to Barcelona. Both days will be a full day travel as most of the trains would be regional trains - Any trip on the direct TGV from Paris will cost a lot in reservation fees.

Much as it disappoints me to say this, you should consider flying or taking 2 days and enjoying the train experience.

Your original post talks about getting a night train anywhere, with Barcelona as an example.

From northern Italy there are plenty of night trains available, but as noted above, none that will get you anywhere near Barcelona.

Have a look at this page for routes south through Italy.  There are other trains that go north - check out the brochure on nightjet.com