The "Steel Soul" mode usually only opens on a second playthrough.
If you go to the "Advanced" tab in the main menu of Hollow Knight: Silksong, and then enter the combination "up, down, up, down, left, right, left", then the hardcore mode with permanent death "Steel Soul" will become available. No respawns for Hornet.
Meanwhile, other players are complaining on Steam about the high difficulty of Silksong, forcing them to abandon the new metroidvania. Some even believe that the game needs to be completely reworked.