Greetings,
Welcome to the forum.
I am not a HP employee.
There are no Windows 10 BIOS updates for your PC. BIOS version 5.16 is it.
A 2.5 inch SATA SSD should work. Your PC has a NVIDIA GeForce 9100 chipset so anything is possible.
Any SATA device should work on a chipset that supports SATA storage devices. Per Nvidia this chipset supports SATA 3.
So the questions are; does the BIOS see the drive? And, how are you deploying this drive?
You would have to initialize and format the drive in Windows Disk Management to see the drive in Windows File Explorer if this device is being used as a secondary data device.
Or you could copy/clone the existing Windows 10 HDD image to the new SSD. The new SSD having a correctly cloned OS image should boot to Windows without requiring Windows Disk Management intervention in this scenario.
Regards