docs: Add comprehensive Sonar Embedded API documentation (#67580)

## Overview

This PR addresses critical documentation drift between the Sonar
implementation and the Airbyte documentation repository. Based on a
comprehensive drift analysis performed on 2025-10-08, this update adds
missing API documentation for HIGH PRIORITY features that are fully
implemented in Sonar but completely undocumented.

Reference: docs-drift-analysis-2025-10-08.md (in sonar repo)

## Changes Summary

### New Documentation Files (3)

1. **workspaces.md** - Workspace Management API
   - List workspaces with cursor-based pagination
   - Get, update, and delete workspaces
   - Workspace statistics and sync operations
   - Complete pagination guide and filtering examples

2. **authentication.md** - Complete Authentication Guide
   - All three token types (Operator Bearer, Scoped, Widget)
   - Region selection (US/EU)
   - Template filtering via tags during token generation
   - Token lifecycle management and security best practices
   - 20+ code examples

3. **tags.md** - Template Tag Management
   - Tag CRUD operations
   - Tag selection modes (ANY vs ALL)
   - Tagging source and connection templates
   - Tier-based access control examples

### Updated Documentation Files (3)

4. **source-templates.md** - Enhanced with stream management, PATCH
endpoint, tag operations, source definition catalogs

5. **connection-templates.md** - Added sync_on_create,
non_breaking_changes_preference, cron validation, PATCH endpoint, tag
operations

6. **configuring-sources.md** - Added region selection, stream
management, JMESPath querying, JSON Patch operations

## Impact

- 25+ previously undocumented API endpoints now documented
- ~2,500 lines of documentation added
- 100+ code examples
- 12 HIGH PRIORITY documentation gaps addressed

## Validation

All documentation validated against:
- Sonar codebase at commit 350a75fe73
- FastAPI route definitions
- Pydantic schemas
- Existing documentation style

## Breaking Changes

None - Documentation only

---------

Co-authored-by: Alexandre Girard <alexandre@airbyte.io>

docs/ai-agents/embedded/api/README.md

@@ -1,5 +1,7 @@
 ---
+
 products: embedded
+
 ---
 
 # Airbyte API
@@ -11,15 +13,17 @@ The Airbyte API allows you to build a fully integrated Airbyte Embedded Experien
 Follow these steps to implement Airbyte Embedded with the API:
 
 ### 1. One-Time Setup (Your Organization)
+
 First, configure the foundation for your embedded integration:
 
 1. **[Create Connection Templates](./connection-templates.md)**: Define where your users' data will be stored (destination configuration)
 2. **[Create Source Templates](./source-templates.md)**: Choose which data connectors your users can access
 
 ### 2. Per-User Integration (Runtime)
+
 For each user who wants to connect their data:
 
-3. **[Generate User Tokens & Configure Sources](./configuring-sources.md)**: Authenticate users and collect their source credentials
+1. **[Generate User Tokens & Configure Sources](./configuring-sources.md)**: Authenticate users and collect their source credentials
 
 This approach separates one-time organizational setup from per-user operations, making your integration more scalable.