SSD appears in BIOS and Device Manager but not in Disk Management or any other tool

Question

After a crash a few days ago, my SSD wasn't detected in the BIOS (or anywhere) anymore for a while.

After trying everything, I decided to try to put it in the oven to re-flow the solder before tossing it, and it actually "worked". The disk is visible again in the bios (every time, reliably), and in the Device Manager on Windows (installed on another HDD), correctly recognized as "SanDisk SDSSDA240G", displayed as working correctly.

Problem is, no drive letter is showing up. If I open the Disk Management tool, the disk isn't there (not even as unallocated space).

I also tried a bunch of tools, and none can see the disk exists :

• Diskpart : list disk (both from Windows and from WRE booting from install disk)
• Testdisk (both from Windows and from booting on a USB flashdrive Linux distro)
• Partition Wizard (from Windows)
• fdisk, hwinfo, ... (from Live Linux)

I'm probably forgetting more, but they all have the common point of acting as if the disk wasn't plugged in at all and not listing it anywhere, despite it appearing in the BIOS (and in Devices Manager).

After activating SATA hotswap, I was able to have the disk actually show up on Testdisk (booting from flashdrive) by pluggin it after boot, but when I tried scanning it it gave a "Read error" on every sector.

If I hotplug it on Windows, the new device sound plays correctly and it appears in the Device Manager, but that's it.

It's probably hopeless but if anyone has an idea, I'll try anything at this point! Thanks

OS: Windows 10 x64 Pro
Devices Manager :

SSD : Sandisk SSD Plus 240G
MB : MSI Z68S-G43 (G3)

Edit : Forgot to mention : I have an USB enclosure, and the problem is exactly the same with it (Gets installed successfully after plug-in and shows up in the devices manager, but only there)

Edit2 : Anyone has a Sandisk SSD Plus 240GB? I wanted to try flashing the firmware, but SanDisk only lets you download a bootable firmware installer if it can detect the SSD in the Windows tool... (Sandisk SSD toolkit)