windows - Initialize a not working disk

I have a 1TB 2.5" HDD causing me some trouble. I am using an external case connected to my computer through USB3. The case and the cable are working. I tried them with another working HDD.

On the disk management tool, I can see my problematic disk (Disk 2):

If I try to initialize it using a MBR partition, then a GPT one. In both case, I get the following error:

The request could not be performed because of an I/O device error.

On the device manager I tried to update the driver, but the best drivers for your device are already installed.

I also searched for updated drivers on Windows Update without success. Beside, uninstalling the device did not help.

Disk 2 does not have an assigned letter, so afaik, I cant use chkdsk X: /r.

Lets see if DISKPART can help. Running LIST DISK prompt:

DISKPART> LIST DISK
  Disk ###  Status         Size     Free     Dyn  Gpt
  --------  -------------  -------  -------  ---  ---
  Disk 0    Online          476 GB  1024 KB        *
  Disk 1    No Media           0 B      0 B

Disk 0 is my main disk. We have Disk 1 from the Disk Management tool. Disk 2 is not here. At that point, maybe we should dig into what is Disk 1. Is there a link between Disk 1 and Disk 2? Does fixing Disk 1 will solve the problem?

Selecting Disk 1 and creating a primary partition there will prompt this:

No usable free extent could be found. It may be that there is insufficient
free space to create a partition at the specified size and offset. Specify
different size and offset values or don't specify either to create the
maximum sized partition. It may be that the disk is partitioned using the MBR disk
partitioning format and the disk contains either 4 primary partitions, (no
more partitions may be created), or 3 primary partitions and one extended
partition, (only logical drives may be created).

It seems legit because DISKPART already show that DISK 1 has 0B free. Alright.

Most search I made online went to website promoting their own solution like aomei, partition wizard or minitool. I would like to use windows directly or to rely on a FOSS solution.

Feel free to ask more precision or information in comment, I will update this post to add them.

Answer

Lets try CrystalDiskInfo as recommended by @bertieb on the SU chat:

According to the Wikipedia's SMART page:

Count of "unstable" sectors (waiting to be remapped, because of unrecoverable read errors). If an unstable sector is subsequently read successfully, the sector is remapped and this value is decreased. Read errors on a sector will not remap the sector immediately (since the correct value cannot be read and so the value to remap is not known, and also it might become readable later); instead, the drive firmware remembers that the sector needs to be remapped, and will remap it the next time it's written.[57]

However, some drives will not immediately remap such sectors when written; instead the drive will first attempt to write to the problem sector and if the write operation is successful then the sector will be marked good (in this case, the "Reallocation Event Count" (0xC4) will not be increased). This is a serious shortcoming, for if such a drive contains marginal sectors that consistently fail only after some time has passed following a successful write operation, then the drive will never remap these problem sectors.

At that point, I dont want to rely on a problematic disk. One 1TB HDD is quite cheap nowadays. I will follow @DanielB's advice and ditch the old one and buy another.