I do not see how else you can call the pressure differential created by the propeller other than a form of energy storage.
I would not call it energy storage - but I see why you are saying that.
There is loop but it is as follow (proportions are just an example).
Wind power available to vehicle will be split say in two equal parts. One half accelerates the vehicle directly thus ends up as kinetic energy the other half will be taken from wheels and sent to propeller witch then increases the pressure differential
I'm not sure I agree with the proportions but, as you say, they are just to illustrate the example. The important part here is they represent two non-zero values.
(you can look at this as increasing the apparent wind speed relative to vehicle).
You have just given the answer as to why the Blackbird could be capable of exceeding wind speed.
While ever the Blackbird is moving, the propeller will always produce this pressure (also known as thrust) which means the "apparent wind speed" (as you have called it) which the Blackbird experiences will always be greater than the actual wind speed.
All your claims about the Blackbird's abilities (or lack thereof) are 100% correct if you were to use this "apparent wind speed". It could never exceed the "apparent wind speed" for any length of time, if at all.
... ... ...
For blackbird since it takes in this example half of the available power and stores that as pressure differential basically increasing the available potential energy it allows the blackbird to exceed wind speed for some limited amount of time as when above wind speed direct downwind there is no longer any wind power available to vehicle and it is starting to use the energy stored as pressure differential but it will continue to use just half of the power provided by the pressure differential to accelerate (increase kinetic energy) and then the other half it will put back in to increasing the pressure differential.
Again, I'm not enthusiastic about some of the terminology and I'd be cautious about the proportions used - but as a
qualitative description, that's not too bad.
Obviously since only half is put back the overall pressure differential will drop and vehicle acceleration rate will continue to drop
(Again, proportions) - But this is not unexpected. Acceleration will tend to zero.
until there is not enough
As in not enough "pressure differential" (as you call it) to provide acceleration? I can agree with that. There will be a point where everything balances out. This will be the "steady state" situation I was asking about earlier.
and it will need to start to slow down.
Now this statement is where (as I see it) you have made your error.
When acceleration drops to zero, it does not mean the Blackbird slows down. It means the Blackbird's velocity does not change. As long as the wind blows the same, it will continue at that same speed.
As long as the Blackbird is moving, it is continually producing (not storing) this "pressure differential" as you call it and the "apparent wind speed" will be greater than the actual wind speed.
How this translates into the Blackbird's final velocity is very dependent on the proportions you mentioned. These proportions and the mechanisms that determine them need to be properly worked out.