Update plugin installation doc to have correct sequence of steps

Signed-off-by: Danil Grigorev <danil.grigorev@suse.com>

Makefile

@@ -499,6 +499,7 @@ upload-staging-artifacts: ## Upload release artifacts to the staging bucket
 update-helm-plugin-repo:
 	./hack/update-plugin-yaml.sh $(RELEASE_TAG)
 	./hack/update-helm-repo.sh $(RELEASE_TAG)
+	./hack/publish-index-changes.sh $(RELEASE_TAG)
 
 .PHONY: promote-images
 promote-images: $(KPROMO)

docs/book/src/02_installation/01_plugin.md

@@ -12,19 +12,38 @@ The `cluster-api-operator` plugin can be installed using krew, the kubectl plugi
 
 1. Add the cluster-api-operator plugin index to krew:
 ```bash
-clusterctl krew index add operator https://github.com/kubernetes-sigs/cluster-api-operator.git
+kubectl krew index add operator https://github.com/kubernetes-sigs/cluster-api-operator.git
 ```
 
 2. Install the cluster-api-operator plugin:
 ```bash
-clusterctl krew install operator/operator
+kubectl krew install operator/clusterctl-operator
 ```
 
 3. Verify the installation:
 ```bash
-clusterctl operator
+kubectl operator
 ```
 
-This should print help information for the clusterctl operator plugin.
+This should print help information for the kubectl operator plugin.
 
-The `cluster-api-operator` plugin is now installed and ready to use with both `kubectl` and `clusterctl`.
+The `cluster-api-operator` plugin is now installed and ready to use with `kubectl`.
+
+### Optionally: installing as a `clusterctl` plugin
+Typically the plugin is installed under `~/.krew/bin/kubectl-operator`, which would be present under your `$PATH` after correct `krew` installation. If you want to use plugin with `clusterctl`, you need to rename this file to be prefixed with `clusterctl-` instead, like so:
+```bash
+cp ~/.krew/bin/kubectl-operator ~/.krew/bin/clusterctl-operator
+```
+
+After that plugin is available to use as a `clusterctl` plugin:
+```bash
+clusterctl operator --help
+```
+
+## Upgrade
+
+To upgrade your plugin with the new release of `cluster-api-operator` you will need to run:
+
+```bash
+kubectl krew upgrade
+```