01-tutorials - [Bug] Auth Failure due to expired Bearer Token in the MCP Server Clients

**In which component is this bug present?**

- [x] 01-AgentCore-runtime
- [ ] 02-AgentCore-gateway
- [ ] 03-AgentCore-identity
- [ ] 04-AgentCore-memory
- [ ] 05-AgentCore-tools
- [ ] 06-AgentCore-observability
- [ ] 07-AgentCore-E2E

If you are reporting multiple bugs, please create a separate issue for each. For documentation improvements, use the documentation improvement issue type.

**Bug Description**
A clear and concise description of the bug.
```
The `bearer_token` stored in SecretsManager expires in about an hour for the MCP server implementation. The remote client that use this token will work as expected for an hour but will error out after the token expires. Users who want to play with the example and tweak the code may need longer than an hour to try things out and will not have a way to run the remote client to test their changes.
```

**Screenshots**
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