I feel your pain...
I’ve had 2 variations on this theme: 1 with WiFi and 1 with Hotspot. As u say ControlCenter gets out of sync with Settings. Both can simultaneously have a different value. More often than not On in settings, but Off in ControlCenter & u have 2 faff around 2 get it working.
People offer all sorts of suggestions about restarting etc and sometimes it helps; but it invariably starts misbehaving after a matter of days or weeks.
WiFi has been fine 4 me now 4 quite a while. But, like u, now Hotspot is misbehaving.
I don’t agree with people who suggest: maybe it’s off because there’s no device connected. Because, IMHO, Hotspot being enabled means your iOS device is discoverable... later u can c how many devices r connected. But if it switches itself off... it becomes undiscoverable.
On the bright side, for me at least, my symptoms don’t seem quite as severe as yours. Once I switch mine back on... and I connect 2 it, from 1 of my devices... at least mine will usually stay on & connected.
if a connection drops due 2 a glitch... fair enuff... but don’t go undiscoverable...