As you formatted it through Windows install, I don't remember there is any way you could overwrite the data
unless you wrote something new onto it or hooked the command console and specifically told diskpart to overwrite, other than that the data should be still there. All three tools you mentioned are file-level recovery software, this means they need a partition to work on. But in your case partitions are also gone. So you need to rebuild them. (That is what I assume, as you told you deleted the partition)
Before we proceed, some words of caution. Right in that moment, every single bit you write on that drive will risk the deleted files. DO NOT write/delete ANYTHING on/from the drive. Don't run/install/format Windows on it. Don't install anything on it. Don't even joke about doing it. Best grab a second drive, install Windows on it then hook the deleted drive. For the paranoid, you can take a CLONE (not an image, it really mixes up in concept) of the drive using a bootable cloning software such as CloneZilla. It'll take a snapshot of every bit on the drive. If you screw the restorable data you can just rewrite the image and try again. That'll need another drive of the same size, fully empty. Oh, also, when restoring deleted data, don't restore to the same drive.
Let's try up TestDisk to see if the partitions are still there. Here is a step-by-step guide on restoring partitions:
https://www.cgsecurity.org/wiki/TestDisk_Step_By_Step