I'm not parent, but Overwatch runs very well on my computer with Wine + DXVK (Wine plugin(?) which translates DirectX to Vulkan). Performance is not noticeably worse than Windows.
If you have a laptop with switchable graphics, you will need to use nvidia-xrun to enable Vulkan passthrough to the dGPU, but aside from that I just followed these instructions: https://github.com/lutris/lutris/wiki/Game:-Overwatch
Note that the Blizzard app will fail to launch with DXVK enabled, so you have to disable DXVK, launch Battle.net, enable DXVK, and then click the 'Play' button to start Overwatch. I made a few scripts for this, so I just do `./disableDxvk ... ./startBlizzard ... ./enableDxvk ... click play` to run the game.
WINEPREFIX=~/.overwatch_wine/ setup_dxvk64 # enable DXVK
WINEPREFIX=~/.overwatch_wine/ winecfg # disable DXVK: delete the overrides from Libraries tab
exo-open Battle.net.desktop # launch the Blizzard app, the .desktop should be generated on install
Have you had any luck running it with Wine?