Was the plan merely to take European Soviet Russia and dig in at the edge of Asiatic Soviet Russia? Or was there an eventual plan to take and hold all of the Soviet Union?
The immediate plan for Barbarossa was to take and occupy up to an imaginary line between Arkhangelsk and Astrakhan. Exactly where this would fall was unclear. Sometimes this is also called the Volga line, as it was expected that the Volga would form the southern half of the line. Further operations... or a negotiated settlement was expected to follow.
Exactly where the final border was going to be is unclear, and likely remained unclear to the German high officials. It definitely included the Urals as they are mentioned in Generalplan Ost. The Germans also came to an agreement with Japan that divided Asia along longitude 70° E. everything West of that was Germany's sphere of influence. So again we get a glimpse that they anticipated expanding grab only the western half of the country.
There's no sign that anyone in Germany was anticipating the complete conquest of all Soviet territory except in the very distant future.