10 bit + hardware encoder

Linux Mint 22.1
CPU - Intel Core i9-13900h
GPU - Intel Iris XE 96

I want to export video with hardware codec in 10-bit format. But I have encountered problems that I cannot solve on my own. My integrated Intel Iris XE graphics chip is not old, it supports vaapi hardware acceleration in 8-bit without problems (h264 and hevc).

Flatpak Shotcut:
When I try to export with the “H.264 High 10 Profile” preset, I get this error:

Gtk-Message: 10:59:09.945: Failed to load module "xapp-gtk3-module"
[h264_vaapi @ 0x785a94001b00] A hardware frames reference is required to associate the encoding device.
Failed with exit code 11
Failed with exit code 11

When I try to do the same in the AppImage version, I get this error:

mlt_repository_init: failed to dlopen /tmp/.mount_shotcuVD74Pu/usr/bin/lib/mlt-7/libmltsox.so
(libsox.so.3: cannot open shared object file: No such file or directory)
[h264_vaapi @ 0x78c6ec001b00] A hardware frames reference is required to associate the encoding device.
Failed with exit code 11
Failed with exit code 11

The regular version from the archive shotcut-linux-x86_64-250511.txz does not find any hardware codecs in my equipment.
My preferred version is Flathub.
Is there a way to make the hardware codec work with 10-bit format?
There are no problems with the software codec, but the hardware one works faster.

Try HEVC. H.264 for 10-bit is actually uncommon.

HEVC:

[hevc_vaapi @ 0x780f50001d80] A hardware frames reference is required to associate the encoding device.
Failed with exit code 11
Export job failed; trying again without Parallel processing.
[hevc_vaapi @ 0x77b1f8001d80] A hardware frames reference is required to associate the encoding device.
Failed with exit code 11
Failed with exit code 11

without Parallel processing:

[hevc_vaapi @ 0x767320001d80] A hardware frames reference is required to associate the encoding device.
Failed with exit code 11
Failed with exit code 11

FWIW, I just tested the Flatpak on a system with AMD Ryzen 7 pro 5850u with integrated Radeon, and HEVC 10-bit failed for me too with a similar error. I have used it successfully on Windows with NVENC. Videotoolbox on M1/macOS worked as well.