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The illusion of 3D shape and texture in a 2D medium is created with contrast of shadows and highlights. Because the lighting was indirect and diffuse what these lack are the sparkle of specular highlights which would provide stronger and more natural clues about the shape and texture.
Part of the problem in your shots is even the focal points aren't very sharp due to focusing error or camera / subject movement during the exposure. But even with a sharply focused shot the inherent nature of the RGB mosaic sensor and anti-alias filter over it will "mush up" the tiny specular reflections we see by eye on objects like flower petals, fur and feathers and the captured photos lose the seen-by-eye sparkle. That's what is missing in these.
For example, I was mindful of the role of specular highlights in creating the illusion of 3D when taking this flower shot at the Botanical Garden in DC:
It was taken with dual flash, one on the bracket over my camera, the other held behind the flower in my outstretched left arm. It is the sharp highlights, more than the shadow gradient, which reveal the shape and texture of the flower and the water drops which would have been missing had I shot with the diffuse ambient light in the room. There was sufficient light intensity but it had the wrong characteristics for the desired 3D look I wanted.
As a general rule of thumb when an object is soft like a flower you'll want smaller direct collimated (parallel) sources at angles to the the lens that will create specular reflections to create the illusion of shape and texture. Fur and feathers are hard surfaced objects but for them to appear soft, fuffy and 3D in a 2D photo you'd also want to light sources / angles which create the same specular sparkle on the tiny facets on the hairs and feathers.
The reason larger diffuse sources are used for applications like human portraits is to hide those specular clues about texture and with them the wrinkles and bemishes.
Another difference in lighting strategy between human and still life is that with humans there's a need to keep the main "key" light vector in front to highlight the eyes and mouth. But in terms of overall illusion of 3D shape of a 3D object in a 2D photo the better strategy is to shoot into the shadow side of a backlit subject as illustrated in this studio lighting exercise:
Above the strongest sources creating the highlights are behind coming from right and left with flat fill in front to open up the shadows. Here's a similar strategy to create the illusion of 3D done with just the light of a window and a silver reflector out it front, above and to the left:
By moving the reflector to the left (opposite the key direction) I was able to use it to create both a degree of "key" modeling on the front side, and overall fill to allow the camera sensor range to record the detail in the shadows similar to how it would be perceived by eye. I set-up that egg shot to illustrate to another FM poster how to light a maternity shot without the mother-to-be winding up looking like a beached whale. The chickens were the stand-ins for the father-to-be looking on in the background.
Next time try some flower shots in direct sun behind the flowers. In front either use flash for fill or cover a piece of cardboard with aluminum foil to create a specular reflector which will add specular peaks within the shadows it fills. The foldable silver mylar reflectors sold to cover car windows in the summer are ideal for this. Also useful are smaller hand mirrors you can use to bounce the backlight back onto the front side to create a "spotlight" effect.
In terms of composition of a shot like this the "star in the spotlight" metaphor is something to keep in mind. Spotlights are used on stages to guide the audience to the star of the show and keep them focused. The overall contrast gradient of tone and color do the same in a photo of flowers. The flower or part of the flower that contrast the most in tone or color from all the rest will naturally pull the viewer there.
When you introduce a second bunch of flowers in the background, separated horizontally from the main one as in your first shot what you set up is a dynamic where the viewer will first see the focal point in the foreground then wander off it to the smaller, less sharp and less interesting secondary focal point in the background. That lessens the impact of the main focal point.
A way to provide context of the other flowers behind but not make them pull attention off is to compose the shot with the background object behind, not off to the side as with the chickens in my egg shot. When the context is put directly behind it will be seen holistically while focusing on the main focal point and the viewer's brain will not tell the eyes to go explore what winds up being less interesting parts of the frame. When the eyes do wander off the fact they don't find any interesting contrasting distractions to dwell on will make them more likely go back to the main focal point for a second look.
Making a single flower group stand out in a sea of similar flowers can be done with a combination of selective DOF and lighting, putting the "star" in the spotlight of brighter lighting. That's where the hand mirror mentioned above would be useful as the "spotlight". But you can create the same effect in post processing by exposing the focal point normally then burn in and desaturate the background flowers a bit to make them seem less interesting by comparison so the viewer dwells and keeps coming back to what you want to be the star of the show.
That of course implies that before taking the shot you decide which grouping or part of a single flower you want to be the star then plan the composition / lighting / post processing strategies around that goal.