Although the printer sends at starts the message that host action commands are supported (Recv: Cap:HOST_ACTION_COMMANDS:1) octoprint seems not to enable them.
What did you already try to solve it?
I updated the printer firmware to the one from may 2023.
OctoPrint doesn't have to "enable" anything - if the printer sends a host action command, OctoPrint will respond. For example, if you click pause on the printer's display, it should send a command to OctoPrint to pause the print. If this does not happen, then there is something wrong within the printer firmware.
Well at startup octoprint receives "Recv: Cap:HOST_ACTION_COMMANDS:1".
So I thought okay, the printer sends that host action commands work I thought octoprint would then show the buttons and would stop at filament runout.
Shortly after the firmware Update of the printer I had in this section two buttons "Pause" and "Resume".
There are no buttons that should appear there. Host Action Commands are about the printer telling OctoPrint commands, not the other way around.
If you had buttons there before, they were likely from "Custom Controls" (or, a plugin that deals with filament runout) and nothing to do with host commands or your printer's firmware update.