docs: Update Nix installation documentation (#2291)

* docs: Update Nix installation documentation

This changes the documentation to show the provided Home Manager module
instead of manual Home Manager installation instructions. Also fixes a
typo in the NixOS instructions and removes the unfinished and now
unnecessary section on zsh integration via Home manager (since that is
included in the provided module).

* docs: Change example Home Manager configuration

docs/installing/README.md

@@ -35,7 +35,29 @@ nix-env -iA nixos.starship
 
 #### Declarative, single user, via [home-manager](home-manager)
 
-Add `pkgs.starship` to your `home.packages` in your `home.nix` file, then run
+Enable the `programs.starship` module in your `home.nix` file, and add your settings
+
+```nix
+{
+  programs.starship = {
+    enable = true;
+    enableZshIntegration = true;
+    # Configuration written to ~/.config/starship.toml
+    settings = {
+      # add_newline = false;
+
+      # character = {
+      #   success_symbol = "[➜](bold green)";
+      #   error_symbol = "[➜](bold red)";
+      # };
+
+      # package.disabled = true;
+    };
+  };
+}
+```
+
+then run
 
 ```sh
 home-manager switch
@@ -43,20 +65,9 @@ home-manager switch
 
 #### Declarative, system-wide, with NixOS
 
-Add `pkgs.starship` to `environment.packages` in your `configuration.nix`,
+Add `pkgs.starship` to `environment.systemPackages` in your `configuration.nix`,
 then run
 
 ```sh
 sudo nixos-rebuild switch
 ```
-
-### Modifying Init Scripts
-
-#### With Nix and home-manager, using zsh:
-
-Add the following to `programs.zsh.initExtra` in your `home.nix` file, then
-run
-
-```sh
-home-manager switch
-```