I'm pretty sure I have HEVC support

Make sure your file is in an .mp4 container instead of .mkv. MKVs almost always have to be transcoded because the format is so open

You can test HEVC support on this site or by playing back this video

Windows

Make sure you have the HEVC Video Extensions
~~You can also pay $1 for them~~ or grab it from a mirror

Windows/ Firefox

Install the aforementioned HEVC Video Extensions
Make sure you are updated (> 120)
Go to about:config
Change media.wmf.hevc.enabled to 1 and restart Firefox
Search for HEVC in about:support - it should now show Supported