I took screenshots from the desktop and laptop (STM32_driver_versions.zip). The laptop does not have the STM32 BOOTLOADER under Universal Serial Bus Devices. I was able to get the Driver versions installed on the desktop but none for the laptop. I hope these are the correct drivers you're asking for.
I also tried to manually install the drivers for DfuSE as suggested by @Jim Shorney, which I found in my C:\Program Files (X86) folder. I also checked the drivers folder for the STM32CubeProg under my C:\Program Files folder with is installed during the install process. I also manual installed it again. Still the same issues for both.
The process went smoothly on my desktop. After I installed STM32CubeProg which also installed the drivers, it easily recognized the tinySA after I put it in DFU mode. I didn't even have to click the refresh button. So this could be a problem with the drivers for my laptop.
I hope that STM could come up with updated drivers. I sure would like to do my next FW updates on my laptop.
Thank you.
Horace F