IntelliJ 2026.1 EAP now has an option to move files to the trash / recycle bin on deletion.
It’s not active by default, and this is probably a good thing as deleted files could easily accumulate in your trash bin. Find the option here:
Nota: there can be some delay between files deletion and their apparition in your trash bin. At least, this is what I experienced on Arch Linux. I cannot say if this is a problem with my IDE or my system.
One last thing: you can already recover deleted files using the Local History, which is more versatile, but can be corrupted.