API gateway - How can I merge data in APIGateway intergration template language - amazon-web-services

Question

I am trying to enhance data I am pushing through an APIGateway Websocket with information about the connection and user.
The integration is pushing the data into Kinesis for context. I would like to do the following where I can merge the JSON objects together at the top level.
#set($payload = $input.json('$'))
#set($data = "{""apiId"": ""$context.apiId"", ""region"": ""${AWS::Region}"", stage"": ""$context.stage"", ""connectionId"": ""$context.connectionId""}")
{
"Data": "$util.base64Encode({merge data and payload - prefer $data})",
"PartitionKey": "$context.connectionId",
"StreamName": "${EventStream}"
}
The documentation on the available language is awful, there is no reference to an underlying language to look this up. AWS does not link to this from API-gateway but can be found api-gateway-mapping-template, which suggests there is a possible way of doing this with the use of foreach statements:
#set($allParams = $input.params())
{
"params" : {
#foreach($type in $allParams.keySet())
#set($params = $allParams.get($type))
"$type" : {
#foreach($paramName in $params.keySet())
"$paramName" : "$util.escapeJavaScript($params.get($paramName))"
#if($foreach.hasNext),#end
#end
}
#if($foreach.hasNext),#end
#end
}
}
However, my attempt fails serialisation and I can't find any context about the issue in cloudwatch.
#set($payload = $input.json('$'))
#set($data = "{""apiId"": ""$context.apiId"", ""region"": ""${AWS::Region}"", stage"": ""$context.stage"", ""connectionId"": ""$context.connectionId""}")
{
"Data": "$util.base64Encode(
{
#foreach($key in $data.keySet())
#set($value $data.get($key))
""$key"": ""$value"",
#end
#foreach($key in $data.keySet())
#set($value $data.get($key))
""$key"": ""$value""
#if($foreach.hasNext),#end
#end
}
)",
"PartitionKey": "$context.connectionId",
"StreamName": "${EventStream}"
}
the template section does link to websocket-api-selection-expressions but this seems more confusing that helpful.
Is this possible in the template? Or should I simple nest the payload into my data object?