How can I make sure that the steps are placed according to the diagram regardless of my position?

For that you need to use Easy Place mode with the easyPlaceProtocolVersion set to Version 3.

Version 3 accurate placement protocol is only supported in two cases:

• In single player by Litematica itself
• On a server, if the server has the separate Litemoretica mod and the Fabric API mod installed, and your client also has them. So this is only possible on a Fabric based server, not on any Realms, Spigot, Paper etc. servers.

The other pretty common server scenario where the server has the FabricCarpet and CarpetExtra mods, an the accurateBlockPlacement Carpet rule enabled, will only support Version 2 protocol. That protocol version does not handle stair connections properly, it will only set the main rotation of the stair correctly. So in that case you will get wrongly placed stairs sometimes, depending on which order you place them.