feat(lambda): support enums in loggingFormat (#28942)

> # Issue
> > The issue is that LogFormat is a String so it doesn't allow the enum LogFormat. 
> # Solution
> > Created a new enum for the LoggingFormat and added testing. 
So the solution sets these values as potential environment variables.
The main difference is LoggingFormat is assigned to an enum instead of a string.
> # Important Design Decisions
> > This is so that an enum could be used for LoggingFormat without breaking JSII target languages. Some background information is in this pr #28127. Was a recommended solution here. #28127
>
> Remember to follow the [CONTRIBUTING GUIDE] and [DESIGN GUIDELINES] for any
> code you submit.
>
> [CONTRIBUTING GUIDE]: https://github.com/aws/aws-cdk/blob/main/CONTRIBUTING.md
> [DESIGN GUIDELINES]: https://github.com/aws/aws-cdk/blob/main/docs/DESIGN_GUIDELINES.md

Closes #28114.

----

*By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license*

packages/@aws-cdk-testing/framework-integ/test/aws-lambda/test/integ.logging-config.js.snapshot/aws-cdk-lambda-logging-config.template.json

@@ -233,6 +233,112 @@
     "LambdaWithJSONFormatServiceRole37FFB486"
    ]
   },
+  "LambdaWithTextLoggingFormatServiceRole3ADC91E1": {
+   "Type": "AWS::IAM::Role",
+   "Properties": {
+    "AssumeRolePolicyDocument": {
+     "Statement": [
+      {
+       "Action": "sts:AssumeRole",
+       "Effect": "Allow",
+       "Principal": {
+        "Service": "lambda.amazonaws.com"
+       }
+      }
+     ],
+     "Version": "2012-10-17"
+    },
+    "ManagedPolicyArns": [
+     {
+      "Fn::Join": [
+       "",
+       [
+        "arn:",
+        {
+         "Ref": "AWS::Partition"
+        },
+        ":iam::aws:policy/service-role/AWSLambdaBasicExecutionRole"
+       ]
+      ]
+     }
+    ]
+   }
+  },
+  "LambdaWithTextLoggingFormatD614C37E": {
+   "Type": "AWS::Lambda::Function",
+   "Properties": {
+    "Code": {
+     "ZipFile": "foo"
+    },
+    "Handler": "index.handler",
+    "LoggingConfig": {
+     "LogFormat": "Text"
+    },
+    "Role": {
+     "Fn::GetAtt": [
+      "LambdaWithTextLoggingFormatServiceRole3ADC91E1",
+      "Arn"
+     ]
+    },
+    "Runtime": "nodejs18.x"
+   },
+   "DependsOn": [
+    "LambdaWithTextLoggingFormatServiceRole3ADC91E1"
+   ]
+  },
+  "LambdaWithJSONLoggingFormatServiceRole0B3D5672": {
+   "Type": "AWS::IAM::Role",
+   "Properties": {
+    "AssumeRolePolicyDocument": {
+     "Statement": [
+      {
+       "Action": "sts:AssumeRole",
+       "Effect": "Allow",
+       "Principal": {
+        "Service": "lambda.amazonaws.com"
+       }
+      }
+     ],
+     "Version": "2012-10-17"
+    },
+    "ManagedPolicyArns": [
+     {
+      "Fn::Join": [
+       "",
+       [
+        "arn:",
+        {
+         "Ref": "AWS::Partition"
+        },
+        ":iam::aws:policy/service-role/AWSLambdaBasicExecutionRole"
+       ]
+      ]
+     }
+    ]
+   }
+  },
+  "LambdaWithJSONLoggingFormatFA0D6903": {
+   "Type": "AWS::Lambda::Function",
+   "Properties": {
+    "Code": {
+     "ZipFile": "foo"
+    },
+    "Handler": "index.handler",
+    "LoggingConfig": {
+     "LogFormat": "JSON"
+    },
+    "Role": {
+     "Fn::GetAtt": [
+      "LambdaWithJSONLoggingFormatServiceRole0B3D5672",
+      "Arn"
+     ]
+    },
+    "Runtime": "nodejs18.x"
+   },
+   "DependsOn": [
+    "LambdaWithJSONLoggingFormatServiceRole0B3D5672"
+   ]
+  },
   "LambdaWithLogLevelServiceRole90A45743": {
    "Type": "AWS::IAM::Role",
    "Properties": {