Can't see secondary drive anymore

A quick search reveals that it may be a problem with not-updated device drivers/Microsoft .NET Framework/Orphaned Registry entries and accordingly various solutions are suggested. At this point I am not sure whether the laptop (you are connecting the HDD to with the Sata to USB adapter) is experiencing the same problems with other programs too. In any case I am not going to venture into resolving this problem, but rather concentrate on the data recovery aspect.

I am still keen on seeing how that HDD appears in PW. Your drive seems to be playing a hide and seek showing up sometimes in WDM and disappearing and not showing up sometimes. Drive health suspect since Seagate tool did not see it and Crystal Info does not know (unknown.)

Now jettison the Sata to USB adapter and restore the HDD to it original SATA port, Internal.

Check and report whether Windows Disk Management shows it. Install PW on that Desktop and check whether it shows the faulty drive. If it does post the screenshots.

If WDM and /or PW does not see the drive, put Windows to sleep and try to run the bootable Partition Wizard and check.

Download PW Bootable CD Free edition ISO ( not the Server Edition- Demo) from https://www.partitionwizard.com/download.html appropriate to the bit version of your Desktop and create a bootable pendrive with that ISO using Rufus https://rufus.akeo.ie/

Note:
1. Disconnect your faulty drive - if need be - for creating this bootable pendrive on your desktop. You can plug it to the SATA port after that.

2. Make sure you backup any data on the pendrive since all data in it will be lost when Rufus formats the pendrive while writing the bootable ISO to the pendrive.

Boot from the pendrive using the onetime boot menu to run Partition Wizard.

Post a camera/mobile snapshot of how your faulty drive appears in it.