There are many different ways to get WOTS3 to work, but here is the quickest one I've used.
I'll list the other ways below.

NOTE: This may not work for some people but it's worked for me. So if it doesn't work, don't fear, there are more ways.

NOTE: I also installed PhysX from this link https://www.nvidia.com/en-gb/drivers/physx/9_15_0428/physx-9-15-0428-driver-uk/
I don't know if it changed anything though because when I downloaded it, I couldn't find it on my desktop.

1. Navigate in files to Program Files (x86), Steam, steamapps, common and then Way of the Samurai.

2. Find the desktop shortcut file called WayOfTheSamurai3 and make sure it's the one with the icon of your character.

3. Go into its more options and go into properties, then go into the compatibility section and tick the box that says "Run in 640 x 480 screen resolution". Click apply and OK and close files.

4. Now start up Way of the Samurai and see if it worked!

If this did not work for you, there are other ways to get it working.

Here is a bug workaround discussion made by the developers:
https://steamhost.cn/steamcommunity_com/app/427510/discussions/0/4658391921147367300/