Same issue here with World of Tanks Blitz using Proton 6.3-4 and Experimental.
info: Game: wotblitz.exe
info: DXVK: v1.7.3-37-g3f91cdbc
info: Built-in extension providers:
info: Win32 WSI
info: OpenVR
info: OpenXR
warn: OpenVR: Failed to initialize OpenVR
info: Enabled instance extensions:
info: VK_KHR_get_surface_capabilities2
info: VK_KHR_surface
info: VK_KHR_win32_surface
info: D3D11CoreCreateDevice: Probing D3D_FEATURE_LEVEL_11_0
info: D3D11CoreCreateDevice: Probing D3D_FEATURE_LEVEL_10_1
info: D3D11CoreCreateDevice: Probing D3D_FEATURE_LEVEL_10_0
info: D3D11CoreCreateDevice: Probing D3D_FEATURE_LEVEL_9_3
info: D3D11CoreCreateDevice: Probing D3D_FEATURE_LEVEL_9_2
info: D3D11CoreCreateDevice: Probing D3D_FEATURE_LEVEL_9_1
err: D3D11CoreCreateDevice: Requested feature level not supported

Adding WINEDLLOVERRIDES=dxgi=n to the starting options resolves the issue - see section Workarounds in the first issue comment.
I was having problems getting Twilight Struggle, a Unity game, running on Steam/Proton Experimental with Ubuntu 21.04. With Ubuntu 20.10 I had been using PROTON_USE_WINED3D11=1 %command% as the configuration string. That worked with Ubuntu 21.04 for a period of time after installation because I appended --xwayland to the configuration string. Then it stopped working under both XWayland and XOrg.
Reading this issue I found that WINEDLLOVERRIDES=dxgi=n %command% allows the game to run under XOrg and adding --xwayland works under XWayland but at a much lower frame rate, like 1 FPS.
I am experiencing the same issue, except that the workaround does not seem to work for me. I can confirm that using proton version 5.0-10 works fine under Wayland, but anything higher than that does not.
Edit: Steam Runtime Diagnostics: https://gist.github.com/Ristovski/016710a5e5ccb6b32a2e3cc93caf0eb7
Hello @Ristovski, please copy the contents of Steam Runtime Diagnostics from Steam (Steam -> Help -> Steam Runtime Diagnostics) and put it in a gist, then include a link to the gist in this issue report.
I have updated my original comment.
Furthermore, I can confirm that vulkan works fine inside the flatpak environment via flatpak run org.freedesktop.Platform.VulkanInfo.
Looking at the diagnostics information, there's some kind of snafu with XCB connections and Steam Linux Runtime interaction with Flatpak. (https://gist.github.com/Ristovski/016710a5e5ccb6b32a2e3cc93caf0eb7#file-gistfile1-txt-L3723)
Please open a new issue report in https://github.com/ValveSoftware/steam-runtime/ focusing on that XCB detail.
proton experimentalx1 2021-05proton 6.3-4x1 2021-05WINEDLLOVERRIDES=dxgi=nx2 2021-05PROTON_USE_WINED3D11=1x1 2021-05WINEDLLOVERRIDES=dxgi=n`x1 2021-05WINEDLLOVERRIDES=dxgi=n %command%x2 2021-05PROTON_USE_WINED3D11=1 %command%x1 2021-05
Direct3D 11 games are crashing while starting on Wayland with Proton versions 5.13-6 and 6.3-3.
My test results
:heavy_check_mark: Works
:x: Doesn't work
Games tested
Workarounds
WINEDLLOVERRIDES=dxgi=n %command%(Actually works!!, but why?)Logs / Screenshots
Beat Saber and SynthVR:

NieR: Automata

Autonauts
Log
More
vulkaninfo