How do I make macOS properly blacken my TV screen on standby I have a Mac Mini connected to a Sony W755C TV by HDMI. If I put "Set display to sleep" on the Mac, the TV goes to black but displaying a very unsightly OSD text "HDMI 1 (Clock) No input. Check your cables, etc." which stays on forever, until I power the TV off manually. I can't find any menu items in the TV to remove the OSD, which just looks ugly on the huge TV in my living room.

So I tried to use the TV's own "standby if inactive for n hours", but "inactive" for the TV means not fiddling with the remote, which I only use for ON/OFF. The TV is oblivious to what's going on on the Mac. So it will suddenly suggest to sleep in the midst of a movie, which is obviously annoying.

Is there any way I can make the TV either a) go to standby modus without any OSD text, or b) soft-power off (same as pressing OFF on the remote -- which is not full power off, mind you...)
The message "HDMI 1 (Clock) No input. Check your cables, etc." is apparently generated by your TV.  The first place I'd look is in the TV's menu system.  See if there's any way to change what is displayed when there is no incoming HDMI signal.

If you can't find anything there, you can look at the Sony website.  Note that there's a firmware update available for you TV as well.  There's a chance you'll be able to control the "no input" message more easily after the update.

https://www.sony.co.uk/electronics/support/televisions-projectors-lcd-tvs-android-/kdl-43w755c#manuals

But, what you really want, I think, is to set up the Mac Mini so that it shows a blank image as its screensaver.