Constant TAS versus constant GS: What is the influence on turning circle? Scenario

Lets imagine a 50kts wind from east.
Now lets imagine an aircraft flying at 200kts (True Air Speed) east that make a 1.15G turn -90º to north. Maintaining in all moments the given constant speed.

Now, lets imagine the same flight but with 200kts constant ground speed.



In the first case, the speed is 200kts TAS= 150kts GS, and after the turn TAS=GS=200kts
In the second case, the speed is 200kts GS = 250kts TAS, and after the turn, TAS=GS=200kts

Any mistake until now?

The question:
The question is how that influence the turning circle? In which of the two cases the turning circle is flatten/stretched and in which is circular if any? What is the approximate shape of them?

Further explanation

Considering my very weak understanding, the turning circle G depend on absolute speed (~ Ground speed), and thus, turning with a constant ground speed imply a circular turning. Which is independent of the wind. Of course, the pilot would have to accelerate/decelerate to maintain this speed.
With TAS, the real speed is variable, so in our case, I expect to see a turning circle which is horizontally flatten.

But, using a planning system, the result I observe is the reverse: the circle is constant (independent of wind, circular) on TAS and variable (dependent on wind, shape is not drawn) in GS.

Edited: TAS=GS=200kts: I just realized that it is not really true, cause the aircraft need to head slightly east to compensate the wind, so probably the TAS will be ~206 and GS 200. Even if that do not make a big difference for the question.
If you maintain a constant bank angle (30 degrees for a 1.15 g turn) and maintain constant true airspeed of 200 Knots, your path will be as shown in the chart by the yellow line. 

If you maintain a constant ground speed (150 knots) and a constant acceleration 1.15, then your path will be as described by the grey line. It will be as if there is no wind, however it requires thrust variations and bank angle variations.