fix(mcp): PyAirbyte MCP sync_source_to_cache fails with AirbyteConnectorConfigurationMissingError

# PyAirbyte MCP sync_source_to_cache Tool Bug Report

## Summary
The PyAirbyte MCP `sync_source_to_cache` tool consistently fails with `AirbyteConnectorConfigurationMissingError` when attempting to sync data from a declarative connector, even when providing valid configuration parameters.

## Environment
- PyAirbyte MCP v0.31.4 (Python v3.10.16)
- FastMCP version: 2.12.3
- MCP SDK version: 1.15.0

## Bug Description
The `sync_source_to_cache` tool fails during configuration validation at line 603 in `/airbyte/mcp/_local_ops.py` when calling `source.set_config()`. The error occurs regardless of how the `config` parameter is provided:

1. Empty object: `"config": {}`
2. Null value: `"config": null`
3. Omitted parameter (relying on default)

## Error Details
```
AirbyteConnectorConfigurationMissingError: Connector is missing configuration.
Provide via `set_config()`
Connector Name: 'source-rick-and-morty-api'
```

**Stack Trace:**
```
/airbyte/mcp/_local_ops.py:603 in sync_source_to_cache
source.set_config()
↓
/airbyte/sources/base.py:295 in set_config
self.validate_config()
↓
/airbyte/_connector_base.py:176 in validate_config
config = hydrate_config_from_secret_manager()
↓
/airbyte/_connector_base.py:152 in _hydrated_config
return hydrate_config_from_secret_manager()
↓
/airbyte/_connector_base.py:139 in get_config
raise exc.AirbyteConnectorConfigurationMissingError()
```

## Reproduction Steps
1. Create a valid declarative connector manifest (Rick and Morty API example)
2. Call `sync_source_to_cache` with parameters:
```json
{
"source_connector_name": "source-rick-and-morty-api",
"config": {},
"streams": ["characters"],
"manifest_path": "/path/to/rick_and_morty_manifest.yaml"
}
```
3. Tool fails with configuration missing error

## Expected Behavior
The tool should successfully sync data from the declarative connector using the provided manifest file, especially when the connector requires no authentication (empty config spec).

## Actual Behavior
Tool fails with `AirbyteConnectorConfigurationMissingError` during config validation, preventing any data sync operations.

## Connector Manifest Details
The test connector has an empty connection specification:
```yaml
spec:
type: Spec
connection_specification:
type: object
$schema: http://json-schema.org/draft-07/schema#
required: []
properties: {}
additionalProperties: true
```

## Impact
This bug blocks the complete PyAirbyte MCP testing pipeline, preventing:
- Local data synchronization testing
- SQL query testing on cached data
- End-to-end connector validation workflows

## Additional Context
- The Connector Builder MCP tools work correctly for manifest validation and stream testing
- The issue appears to be specific to the PyAirbyte MCP configuration handling
- This was discovered during comprehensive MCP server testing

## Logs
PyAirbyte logs written to: `/tmp/airbyte/logs/2025-09-26/airbyte-log-*.log`
Connector logs written to: `/tmp/airbyte/logs/source-rick-and-morty-api/source-rick-and-morty-api-log-*.log`