Let's address the question based on literal reading of the primary source - Weisung Nr.41 (in English)
As soon as the weather and the state of the terrain allows, we must seize the initiative again, and through the superiority of German leadership and the German soldier force our will upon the enemy.
Our aim is to wipe out the entire defence potential remaining to the Soviets, and to cut them off, as far as possible, from their most important centres of war industry.
Wiping out means eliminating Red Army's manpower akin to what was done in 1941 (Kiew, Wyasma).
Cutting off from war industry in the context of Fall Blau means primarily attacking Maikop, Grozny, and Baku as oil sources (Rostow and Stalingrad were not really unique as industry centers), and cutting Russian lines of communications at Stalingrad.
First, therefore, all available forces will be concentrated on the main operations in the southern sector, with the aim of destroying the enemy before the Don River, in order to secure the Caucasian oilfields and the passes through the Caucasus Mountains themselves.
Should opportunities arise during these operations, particularly by the capture of undemolished bridges, to establish bridgeheads to the east or south of the Don River, advantage will be taken of them. In any event, every effort will be made to reach Stalingrad itself, or at least to bring the city under fire from heavy artillery so that it may no longer be of any use as an industrial or communications centre.
It is obvious that the logic of the document taken literally is quite sound:
- Destroy Red Army reserves.
- After resistance is broken, grab critical military-economical (kriegswirtschaftlichen) resources and deny their use to the enemy.
- Watch what happens.
No. 3 includes numerous possibilities:
- petering out of Russian war effort due to lack of oil;
- cutting Russians off from the overland resupply route;
- gathering enough forces for an attack up the Wolga river;
- getting airfields within range of Russian industry centers in the Urals;
- negotiating a peace with Stalin;
- Turkey entering the war;
- Japan overcoming its fear of fighting Russians;
- positioning forces for a dash to the Persian Gulf to grab British oil supply centers.
The key point here is that it was not possible to predict any of these eventualities with any military-grade certainty. It wasn't even necessary to do so - the victory in the South opened up German decision space immensely and put the Allies into a tight spot.
After the question was edited I went back to another primary source (Franz Halder's war journal), namely his rendition of main points of Hitler's speech at March 28, 1942 planning meeting (not verbatim):
- Fears of Allied landings from Norway down to the Maghreb
- War on Allied merchant tonnage
- Problems with resupplying the DAK. Suppression of Malta
- Fate of the war is decided in the East
- Japanese plans: Ceylon, Australia. Will enter war against Russians if there are enough planes
- ... end goal: closing the Black Sea, line Batum-Baku.
I'd say the part of Japan (this was pre-Midway, pre-Coral Sea!) was much larger in Hitler's plans than that of Turkey. There are no other Mediterranean powers of note (if one nods at Spain and Portugal, oh puhhlease - after Adm.Canaris' shenanigans there was no way for Franco to join the fray).