The MO APYR Wiki claims Blut Royale happens after Panic Cycle according to "the existing order", and Berlin is already controlled by the Soviets by the beginning of the mission. If that is official lore, I suggest changing it into the exact opposite.
The Mermaid's briefing says Tanya was captured after a failed chronoshift attempt after Blut Royale. Since by the time of the Mermaid(1984) chrono backpack is still in prototype phase and Tanya needs to find an AMC to be chronoshifted, it can be safely assumed that Siegfried cannot teleport another person using his Zeitgeist, or he could simply chronoshift in on Zeitgeist(as in convergence), grab Tanya and teleport away. So the only way for Tanya to be chronoshifted in 1982 is the Chronosphere, which is destroyed at the end of Panic Cycle.
Besides, Berlin is in eastern Germany and Black Forest is near southwestern border. According to Sunlight, "Germany has finally fallen after a MIDAS missile destroyed the Black Forest", sounds like Panic Cycle is the last stand of Germany. In Blut Royale, the the SteinsTech assets are carried by technology truck driving off the map, indicating the way to the west is all clear for the Allies. The city is free of Soviet forces until the timer ends, so at the start of Blut Royale the Soviets haven't controlled Berlin. Blut Royale description "The evacuation of Berlin is almost complete" also shows the city is recently under Allied control.
Could Berlin fall after Black Forest? Possible. But it would be more plausible for Berlin to fall before Black Forest. I think Blut Royale shall happen before Panic Cycle, and Berlin shall fall to the Soviets after Blut Royale.
They use the ChronoSphere on the Paradox Engine (by that time is still in the Hangar) to do that, not the ChronoSphere which is destroyed by the MIDAS explosion.