The subject of colour profiles, colour workflow and the technical details of colour fidelity is certainly not something I know and understand much about.
Previous responses to this subject from people who do know about it indicate that uploading a video of any kind to somewhere like discord or twitter(x) will result in file compression and/or file conversion by that website and that colour fidelity can’t be guaranteed or expected because of that.
You might want to look at the Gyan Full Release of ffmpeg that is available here:
https://www.gyan.dev/ffmpeg/builds/ffmpeg-release-full.7z
You can read the technical details of the release here:
Builds - CODEX FFMPEG @ gyan.dev
Edit:Add: I’ve just followed my own advice and read the technical details.
The Essentials Build does have libx264 and can be downloaded here:
https://www.gyan.dev/ffmpeg/builds/ffmpeg-release-essentials.7z
or https://www.gyan.dev/ffmpeg/builds/ffmpeg-release-essentials.zip
(The Full Build has additional libraries in it.)