CfnInclude: Changes to Mappings are recognized by diff but not deployed by deploy

### Describe the bug

While deploying CloudFormation templates using CDK's CfnInclude module I noticed my changes were not deployed, although recognized by `cdk diff`. I see this happen if the only change between deployments is to the `Mappings` block, such as adding keys, updating values, etc.

As mentioned above, I can see the changes being outputted by `cdk diff` but the subsequent `cdk deploy` doesn't deploy changes and reports `No changes`. If I deploy the changes through the AWS Console, everything works as expected.

I tried with the `--method direct` and/or `--force` flags but this leads to another problem - https://github.com/aws/aws-cdk/issues/23141

### Expected Behavior

I expect changes to `Mappings` to be deployed with `cdk deploy`.

1. Make a change to the `Mappings` block in a CloudFormation template
2. Execute `cdk diff` (changes are outputted correctly)
3. Execute `cdk deploy` (changes are deployed correctly)

### Current Behavior

Changes to `Mappings` are not deployed with `cdk deploy`, although recognized by `cdk diff`.

1. Make a change to the `Mappings` block in a CloudFormation template (e.g., add another key to a map in Mappings)
2. Execute `cdk diff` (changes are outputted correctly)
3. Execute `cdk deploy` **(changes are NOT deployed)**

### Reproduction Steps

```python
# stack.py

class DeploymentStack(cdk.Stack):
def __init__(self, scope: Construct, construct_id: str, props: dict, **kwargs) -> None:
super().__init__(scope, construct_id, **kwargs)

template_file = "./template.yaml"

try:
_ = cfn_include.CfnInclude(
self,
"MyStackWithMappings",
template_file= template_file,
preserve_logical_ids=True,
)

except RuntimeError as error:
logger.error("Couldn't parse the template file %s.", template_file)
logger.error("Error: %s", error)
raise error
```

```yaml
# template.yaml

Mappings:
TestMapping:
PolicyName:
test: foo
prod: bar

Resources:
MyBucketPolicy:
Type: AWS::IAM::ManagedPolicy
Properties:
ManagedPolicyName: !FindInMap [TestMapping, PolicyName, test]
PolicyDocument:
Version: "2012-10-17"
Statement:
- Action: "s3:PutObject"
Resource: "*"
Effect: Allow

```

### Possible Solution

_No response_

### Additional Information/Context

_No response_

### CDK CLI Version

2.101.1

### Framework Version

_No response_

### Node.js Version

20.8.0

### OS

MacOS 14.0

### Language

Python

### Language Version

Python 3.11

### Other information

_No response_

Start with the CfnInclude entry point and the stack.py/template.yaml reproduction, then run cdk diff followed by cdk deploy on a Mappings-only change. Done means the mapping change is deployed rather than deploy reporting No changes.

Written by the indexing model from the issue text.