Hi there Teo,
Hahaha, no worries, I'm glad to be assisting you.
I've downloaded your scene file (thank you so much for that), and for this specific case, I'll use any of the following solutions:
Solution A:
-I'd use the Corona Compositing tag, and then I'd create different masks to separate elements (Emeralds, Diamonds, and the metal parts).
-Then, I'll compose them into the video editing software.
Solution B:
-I'd use the Cryptomatte Multi-pass and set it to work in Material mode (as I can see, you already assigned different materials and IDs
-Then, save them as multi-layer EXR images so that you can extract the required multi-pass in your video editing software (assuming you'll be using AE)
Note: For this specific solution, please consider that you'll require a 3rd party plugin for your video editing software to be able to extract multi-passes from EXR files.
Solution C:
-You can always define the Alpha channel for specific materials.
-I mean, you can go to the Metal material, then click on the "Advanced" channel, and set the Alpha to "Always Black"
-Repeat the process for the diamond material
-Lastly, render your images, but save them using an image file format that supports saving the alpha channel.
-This way, your image will look like a regular image, but if you apply the Alpha channel, then your image will be cut out.
I hope this helps.
I'm including a modified version of your file so you can experiment with it.