Issues with HDR with Sony smart TV and the latest Apple TV 4K - colours washed out

Hi, I have received the latest Apple TV 4K a couple of days ago and I'm generally very happy with it :-) Sadly, I have encountered an issue with delivering the correct HDR signal to my Sony Bravia smart TV. It's SONY 65" KD-65XD9305B and it supports HDR10 (no Dolby Vision or HDR10+ or HDMI 2.1 support).

The TV set is 100% successfully tested with HDR10:

• Netflix and other streaming platforms that deliver HDR10 content
• MKV or MP4 HDR10 files etc.
• HDR playback from BD discs with external Sony's BD HDR/3D player via HDMI 2.0b cable > TV

Unfortunately, when I connect Apple TV 4K to the TV, its HDR signal looks washed out of colours and contrast - like the video signal delivered via HDMI (same port and HDMI cable used for the BD player) was not delivered to the TV with a relevant HDR profile/information or the TV doesn't recognize the HDR format.

My steps performed to resolve the issue so far:

• I have performed Apple TV's compatibility test - and it reported the TV supports HDR,
• There are no HDMI signal issues - Apple TV 4K's test performed as well,
• I have tested different settings at Apple 4K's settings in regard to the selection of different 4K formats (SDR works just fine but none of HDR ones),
• I have also tried to select a combination of SDR formats + "Match Dynamic Range" settings.

None of the above worked out and I cannot watch the HDR context with correct saturation and contrast - even though I know that the newest Apple TV 4K supports the HDR10 supported by my TV.

I have also notice that - despite I select SDR + "Match Dynamic Range" settings, eg. Netflix and other platforms choose Dolby Vision format, not "standard" old HDR like it is performed at TV's Netflix and other streaming apps.

I wonder if there's any solution to force Apple TV 4K to use ONLY HDR10 format or if there's any other fix available? I actually find that very non-statysfying such a high-tech and not really cheap newest Apple TV 4K device lacks such basic settings that were available at its older version. As far as I know, it was possible to select non Dolby Vision HDR format. There's no such option in the latest version, unfortunately.

I'd be extremely thankful for any advice that could fix my issue.

Greetings :-)