Try the custom AI to help you find products that Reddit loves.
You have up to 3 drives spots in your Thinkpad. 2 of them are for SSD drives (like chewing gum sticks) and the 3rd is for a traditional laptop drive. This can either be an ssd drive or mechanical drive. I opted for a 1TB SSD drive in that 3rd bay just for speed reasons. You can either add another stick drive using the adapter you bought (more expensive in that format) or purchase the "other" adapter you linked to and install a traditional format drive. I purchased my adapter similar to the one you linked to from Amazon. https://www.amazon.com/gp/product/B01DXK5PAS/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1
It's pretty plug and play to add a drive in that bay using the adapter. 1 to 2 TB drives are pretty cheap for the mechanical ones, or you could get SSD if you wanted the speed. Or get the M2 drive format and use that stick adapter you already purchased. Those are incrementally more expensive however...
I'm from Italy too, and the P series trays used for SSDs and HDDs can be found on Amazon Italy too. I have them saved on a list. I'm going to update this post with the relevant links.