I became a little bit lost in your description of the plan, but it would seem like most any photo software like Photo Shop, Affinity, etc. should be able to do this. It can get complicated, because of the number of steps required, but it gets easier with practice.
If this needs a background photo to which all of these smaller images will be applied, you copy that photo into the software first and it becomes your base layer. Then, each photo of the pieces get loaded into a separate "Layer" within the program and then it's surrounding waste is removed via a "clipping method" leaving only the image itself on the layer. You basically want just the image of the item and not any of it's surrounding background. It's kind-of like clip art (think paper dolls).
A layer is like a piece of clear plastic to which you have just added a small image in it's center, and when assigning each layer you get the ability to label it. So you can label or name each layer by the writing that you added to the back of the object in the original photo of it. Each layer photo is then able to be sized, rotated, enlarged or made smaller, stretched, and even color modified via the software, and your software selects each layer separately from all of the rest of the layers, then letting you go back and fine tune modify each without affecting any of the others. Imagine yourself "stacking blocks" when doing this. You need to think of your photo as having three dimensions when stacking layers.
Clicking on any layer will give you the ability to work on that one layer. So one by one you can adjust, move, place, etc. each image in position above the background photo. Again, the layers are like invisible clear plastic with an image applied to it, so you can stack all of them and still see through the 'no image' areas all the way down to the background photo. Select a layer and position, size it, rotate it, etc. Then select the next layer and repeat the process, etc. until all are ready. There are ways to back up in your steps if you make a mistake, but I also save full progress copies of the file often "as a backup" too.
When all layers have been added and each one processed, you can then save the image with all of the layers held in their right positions, but still allowing later fine adjustments or even the adding of additional layer images. There is even a way to move layers up and down in this stack that you are creating.
You can also flatten all of the layers into the background image. This will reduce the file size, but it will also prevent any further layer modifications, since there will only be a single layer photo with everything combined together. So be absolutely certain that it's final before doing this. For what I frequently do for myself, since I frequently like to edit and improve things, I usually save the large file in it's multi layered file format. Bigger, but safer. Be absolutely certain to label each layer as you create them, or you will get lost quickly.
Making a collage is easily done this way. Remember that each layer can be selected and then adjusted, which gives you the ability to further trim, enlarge, rotate, move etc. without affecting the rest of the layers, yet you can see all of the other layers and background by looking through the clear parts of the layers all the way to the background as if it's a complete final image, yet you will still have the ability to go back and make modifications of each image on it's own layer one at a time by selecting it. In photography, you can put people or things from multiple photos together this way to make one "composite" photo too.
I am a woodworker and woodcarver as well as photographer, but I'm not a very good artist. So I frequently find and clip the desired portions of images that I like and save them as Jpeg files, then paste these line drawing images together to make one total line drawing pattern, using this same layering method. The final assembly then becomes my pattern that looks like I drew it all myself. (Me cheating? Well yea, a little bit.) I then print it on my laser printer using "Overlay Film" instead of paper, which is clear Mylar, but with a clear "peel and stick" backing. This assembled image is then cut out of the printed sheet and positioned and stuck to my piece of wood wherever I want it. I can then carve or cut it out following the lines of this clear applied pattern. When complete, I remove all of the left-over bits and pieces of the pattern before applying a finish or performing additional work.
Charley