Fix HTTP timeouts (#616)

### TL;DR

Updated API base URL from mcp-agent.com to web-internal.mcp-agent.com to reflect recent backend changes

### What changed?

Changed the default API base URL from `https://mcp-agent.com/api` to `https://web-internal.mcp-agent.com/api` across multiple files:
- Updated `DEFAULT_API_BASE_URL` in constants.py
- Updated API URL references in documentation files
- Updated example in API client docstring

### How to test?

1. Verify that the CLI connects to the new API endpoint when running commands
2. Check that documentation examples reflect the new URL
3. Ensure existing integrations continue to work with the new endpoint

### Why make this change?

To fix it

<!-- This is an auto-generated comment: release notes by coderabbit.ai -->

## Summary by CodeRabbit

* **Chores**
  * Updated the default API endpoint to use the internal service endpoint instead of the public endpoint.

* **Documentation**
  * Updated example documentation to reflect the new API endpoint configuration.

<sub>✏️ Tip: You can customize this high-level summary in your review settings.</sub>

<!-- end of auto-generated comment: release notes by coderabbit.ai -->

Author: bryanmdavis25

examples/mcp_agent_server/asyncio/README.md

@@ -189,7 +189,7 @@ andrew_lm@Mac sdk-cloud % uv run mcp-agent deploy basic_agent_server -c /Users/a
 │ Secrets file: /Users/andrew_lm/Documents/GitHub/mcp-agent/examples/mcp_agent_server/asyncio/mcp_agent.secrets.yaml │
 │ Mode: DEPLOY                                                                                                                │
 ╰──────────────────────────────────────────────────────── LastMile AI ────────────────────────────────────────────────────────╯
-INFO: Using API at https://mcp-agent.com/api
+INFO: Using API at https://web-internal.mcp-agent.com/api
 INFO: Checking for existing app ID for 'basic_agent_server'...
 SUCCESS: Found existing app with ID: app_dd3a033d-4f4b-4e33-b82c-aad9ec43c52f for name 'basic_agent_server'
 INFO: Processing secrets file...

src/mcp_agent/cli/core/api_client.py

@@ -57,7 +57,7 @@ def __init__(self, api_url: str, api_key: str):
         """Initialize the API client.
 
         Args:
-            api_url: The base URL of the API (e.g., https://mcp-agent.com/api)
+            api_url: The base URL of the API (e.g., https://web-internal.mcp-agent.com/api)
             api_key: The API authentication key
         """
         self.api_url = api_url.rstrip(

src/mcp_agent/cli/core/constants.py

@@ -25,7 +25,7 @@
 ENV_VERBOSE = "MCP_VERBOSE"
 
 # API defaults
-DEFAULT_API_BASE_URL = "https://mcp-agent.com/api"
+DEFAULT_API_BASE_URL = "https://web-internal.mcp-agent.com/api"
 
 # Secret types (string constants)
 SECRET_TYPE_DEVELOPER = "dev"

src/mcp_agent/data/examples/mcp_agent_server/asyncio/README.md

@@ -189,7 +189,7 @@ andrew_lm@Mac sdk-cloud % uv run mcp-agent deploy basic_agent_server -c /Users/a
 │ Secrets file: /Users/andrew_lm/Documents/GitHub/mcp-agent/examples/mcp_agent_server/asyncio/mcp_agent.secrets.yaml │
 │ Mode: DEPLOY                                                                                                                │
 ╰──────────────────────────────────────────────────────── LastMile AI ────────────────────────────────────────────────────────╯
-INFO: Using API at https://mcp-agent.com/api
+INFO: Using API at https://web-internal.mcp-agent.com/api
 INFO: Checking for existing app ID for 'basic_agent_server'...
 SUCCESS: Found existing app with ID: app_dd3a033d-4f4b-4e33-b82c-aad9ec43c52f for name 'basic_agent_server'
 INFO: Processing secrets file...