chore: update docs and root test

DEVELOPER.md

@@ -83,7 +83,7 @@ Tool type serves as a category or type that a user can assign to a tool.
 
 The following guidelines apply to tool types:
 
-* Should use hyphens over underscores (e.g. `firestore-list-collections` or
+* Should user hyphens over underscores (e.g. `firestore-list-collections` or
   `firestore_list_colelctions`).
 * Should use product name in name (e.g. `firestore-list-collections` over
   `list-collections`).

docs/en/resources/prompts/_index.md

@@ -20,10 +20,10 @@ kind: prompts
 name: code_review
 description: "Asks the LLM to analyze code quality and suggest improvements."
 messages:
-  - content: "Please review the following code for quality, correctness, and potential improvements: \n\n{{.code}}"
-arguments:
-  - name: "code"
-    description: "The code to review"
+   - content: "Please review the following code for quality, correctness, and potential improvements: \n\n{{.code}}"
+ arguments:
+   - name: "code"
+     description: "The code to review"
 ```
 
 ## Prompt Schema

docs/en/resources/sources/alloydb-admin.md

@@ -27,7 +27,7 @@ Authentication can be handled in two ways:
 ```yaml
 kind: sources
 name: my-alloydb-admin
-type: alloydb-admin
+type: alloy-admin
 ---
 kind: sources
 name: my-oauth-alloydb-admin

docs/en/resources/tools/firestore/firestore-query-collection.md

@@ -18,7 +18,7 @@ with filters, ordering, and limit capabilities.
 To use this tool, you need to configure it in your YAML configuration file:
 
 ```yaml
-kind: sources
+kind: source
 name: my-firestore
 type: firestore
 project: my-gcp-project