Yes, it does seem like the HP Pavilion 15-cs2034tu has support for Intel Optane. The module should go here as shown below:
(You may want to verify beforehand if the M.2 slot actually exists)
You will need a Philips M2.0 * 3.0 screw to install it into the M.2 connector. You can probably find one at a hardware store.
Before you install Intel Optane, update to the latest BIOS from your computer's Software and Driver's page. Once the module is installed, install the Intel Rapid Storage Technology Driver from your computer's Software and Driver's page. Check if you need the older driver or the 1903 driver by checking the version of Windows 10 you have by typing into Windows Search winver. Then restart the laptop once Intel Rapid Storage Technology is installed.
Finally, install Intel Optane Memory and Storage Management from the Windows Store on your device. You will need to select the PCIe drive and enable it as Intel Optane.
Just my two cents, I checked the prices for Intel Optane and they seem more or less similar to the prices of conventional M.2 drives, ultimately defeating the whole purpose of using them to accelerate the existing hard drive. I would personally just buy an M.2 SSD and set that as the boot drive. From experience, I have found speeds on purely SSD laptops to be marginally better than those of cheap drives + Intel Optane modules.
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