Stuttgart to Zurich may be DB but I know it is also MAV, the Hungarian
train. MAV has a route that departs from Zurich to Budapest , the
terminus, which does stop in Stuttgart and Vienna, the route I wanted
to take , ie Stuttgart to Vienna last summer on the date I chose but
2nd class reservations I was told for that date (in the summer) at
night were all sold out
Sorrty, but there is a lot wrong here. DB does not operated trains outside of Germany. MAV does not operate outside of Hungary.
That you see a route on a particular railway's website does not imply that they operate the train. All the central European railways basically link in the same timetable database. That is why you can look up for example Vienna to Zurich on DB or, ÖBB or MAV, or NMBS, or NS or SBB and get the same train times each time...
The Zurich to Budapest train btw. does not go anywhere near Stuttgart.
International trains are typically operated jointly by multiple operators. Eg. the above mentiones Zurich to Budapest train will be a SBB train till the Swiss border, with Swiss staff, a Swiss driver, and Swiss ticketting rules applying (so you can take it with any Swiss Domestic ticket or Pass). It becomes an Austrian train in Buchs, as the crew is changed, and then again gets a crew change at the Hungarian border where it becomes a MAV train. The actualy physical trainset used to operate the service is owned by the Austrians though.
So for Stuttgart to Vienna you would just buy your ticket, and get your reservations from DB. And I find it unlikely that the train would be booked out, as that basically does not happen in this part of Europe.
Back Spain. I am sorry to read that you have already bought the Pass. An Eurail Pass is en expensive way to make travel more complicated where it comes to Spain. In fact, if you can return it for a refund, just do so.
Just book your tickets with RENFE. It is easier to get tickets than reservations. RENFE is by far the worst railway company in Europe. They spend billions on making trains faster, and then waste hours of your time with bad scheduling and inefficient procedures.
For Barcelona to Stuttgart I would just fly.