I do not know if the driver you installed supports VA-API. I never go to the AMD website to install the AMD driver on Linux. I use the one made by Mesa in the OS distribution.
After seeing above suggestion, I removed AMD GPU Driver
$ amdgpu-uninstall
Then install Mesa latest driver by adding PPA. Looks mesa drivers are latest.
$ glxinfo | grep OpenGL
OpenGL vendor string: AMD
OpenGL renderer string: AMD Radeon RX 7900 XTX (gfx1100, LLVM 15.0.7, DRM 3.49, 6.2.0-26-generic)
OpenGL core profile version string: 4.6 (Core Profile) Mesa 23.3~git2308190600.caf15a~oibaf~j (git-caf15a3 2023-08-19 jammy-oibaf-ppa)
OpenGL core profile shading language version string: 4.60
OpenGL core profile context flags: (none)
OpenGL core profile profile mask: core profile
OpenGL core profile extensions:
OpenGL version string: 4.6 (Compatibility Profile) Mesa 23.3~git2308190600.caf15a~oibaf~j (git-caf15a3 2023-08-19 jammy-oi
OpenGL shading language version string: 4.60
OpenGL context flags: (none)
OpenGL profile mask: compatibility profile
OpenGL extensions:
OpenGL ES profile version string: OpenGL ES 3.2 Mesa 23.3~git2308190600.caf15a~oibaf~j (git-caf15a3 2023-08-19 jammy-oibaf-ppa)
OpenGL ES profile shading language version string: OpenGL ES GLSL ES 3.20
OpenGL ES profile extensions:
But Hardware encoder is not detected. When I press Detect, it returns “Nothing Found”. Just click on h264_vaapi, hevc_vaapi and tried to export the video. I see same error with bcairns.