exposure – Do I need 1/128 flash power in guide number 43-44 or is 1/32 sufficient?

Those GN are basically the same.
The MAXIMUM range of the flash is the GN / opening stop
So let's make the maths easy.
GN 44m
Aperture f / 2.0 (has a little more going to f / 1.8)

The GN is not regulated.
It can be in several iso
(It's usually an iso 100 rating)

It can be in different lens lengths.
Some flashes to 50 mm nominal
Others use the classification of their maximum zoom, say 105 mm.

For example, a flash can have a GN iof 44m to 70mm
52 m to 105 mm (if it goes so far), but only
44m to 75mm ****
37m to 50mm
32m to 35mm equiv.

Suppose you have a flash that covers an equivalent lens of 75 mm (50 mm in apsc) to 44 m at f / 1
22m in f / 2
11m in f / 4

But what about the range when it is not 100%?
A quarter of the power is half the distance.
For example
100% GN 42m reaches 22m in f / 2
1/2 power
1/4 of power GN 22 Teach is 11m
1/16 of power GN 11m to 5.5 m.
1/64 GN power 5.5m reaches 2.8m
1/256 GN 2.8m power reaches 1.4m

The flashes can go down in AUTO mode
But it seems you want a complete manual control for consistent results

So you can see that you need lower fractions IF you are having close subjects.

Finally, to NOT have a subject on exposed to the light of the flash and a dark background that is not so illuminated.
You would use slow synchronization. (If required)
Basically, you can calculate the necessary lsdttings with NO flash.
If the camera is set for this or 1/3 stops less, your flash will simply kill the shadows
If you set the camera to 3 stops less than the ambient light, then your exposure will be effectively only flash light.

The balance between the AMBIENT light and FLASH ratio in the exposure is basically adjusting the opening / opening / iso rate from -3 points to -1/3
At -3, the environment is DARK and only lights up no matter how strong the flash is configured,

say 1/16 of power, f / 2
The subjects closest to 5.5 m (3 m) will be overexposed.
Subjects about 5.5m will be properly exposed by the flash.
Subjects that exceed 5.5 m (11 m) will not light up with the flash.

The subjects (background) beyond 1 m will be illuminated mainly only by the environmental configuration

Finally, synchronize flash.
(Apart from HSS (fast superimposed strobe light)
Or a leaf shutter.
Your apsc camera will have a MAX flash sync speed
Let's say 1/160 sec.
SS faster than this will not work
Slower than this brings that ambient light.
Which means you can not use your higher shitter speed of 1/4000 sec.
Good thinking, but let's say you can not go faster than the speed of synchronization of your flash.

As you understand, the duration of the flash can be considered short.
The way in which the fast shutter speeds are achieved is that one curtain closely follows the other as a space or slit.
For example, at 1/800 s s, the first curtain begins to OPEN, once it is half way, the second curtain now follows and closes the shutter.
When the first curtain opens completely, the second curtain is already half closed.
At this moment the x-sync flash fires (1/128 power is 1 / 20,000 sec.) HALF of one image that has flash, the other half does not. The second curtain continues and the exhibition closes.

In ss 1 / 2000sec, the second curtain began to close when the first one was open to 10%
Thus, the first 50% open the second is 40% closed
This exposed 10% gap moves down to
1st curtain fully open
2nd curtain 90% closed.
Flash fire
10% of image saw flash

At the maximum speed of flash synchronization
1/160 (or whatever your camera has, this depends on the speed of the curtain)
You have the first curtain open.
1 / 300sec is open
Then the fire flashes
Then, the second curtain begins to close (1/160 second after the first curtain begins to open)

In increments of 1/1000 sec.
0 all closed
1 1st 1/3 open
2 1/2/3 open
3 1st open
3.01 fire flashes
4 finished flashes
5 nothing happens shutter remains open
6 2nd closing curtains of sarts.
7 2nd curtain 1/3 closed
8 2nd curtain 2/3 closed
9 2nd closed exhibition curtain finished

The exposure of 1/160 sec took almost 1/100 sec. The second curtain followed the first curtain with a delay of 1/160 sec.

I hope this helps