Do I need to display nodes on the deployment diagram that are used only during the start of the application? For example, a key vault, the keys from which are cached at the start of the main application. After that, interaction with the key vault is no longer carried out.
No, you don't need it. You will show in diagrams only a part of your model under a certain aspect. And if that aspect does not need some information you just leave it away. Diagrams are always meant to show some aspect, not the whole model. If you were to show everything everywhere you would just confuse the reader, not help him.
Nevertheless, you should create as many diagrams as needed to cover the whole model. So in another aspect you would/should show those nodes (or whatever you left away somewhere else).