I rolled back to 1803 and then repeated the 1809 update via Windows Update Assistant instead of through the Control Panel. Same result. Human Interface Device Service is started.
I have exactly the same lack of Bluetooth media control functionality in 1809 as in 1803, across 2 devices and 3 players (all that I tried) including Windows Media Player.
Sadly, this bug is not fixed. Prior to 1803 these devices were working perfectly.
What Bluetooth headset or device is it, like what's the actual name. Have you tried any other headset? And what media player software are you using? (Spotify, media player, etc)