I also tried the same and getting same result.

By default its taking nvarchar(max) from Json obj but I need bigInt

To resolve this when you add additional column in your source data set and in Mapping click on import schema it will import the schema of the source and also give you additional column in schema you have to change the type of the column as Int64 as shown in below image. in below image you can see after name there is additional means it is an additional column.

After this run your pipeline, It will create additional column with data type bigint .

{
    "name": "pipeline2",
    "properties": {
    "activities": [
    {
    "name": "Copy data1",
    "type": "Copy",
    "dependsOn": [],
    "policy": {
    "timeout": "0.12:00:00",
    "retry": 0,
    "retryIntervalInSeconds": 30,
    "secureOutput": false,
    "secureInput": false
    },
    "userProperties": [],
    "typeProperties": {
    "source": {
    "type": "JsonSource",
    "additionalColumns": [
    {
    "name": "name",
    "value": {
    "value": "@pipeline().parameters.demo.age",
    "type": "Expression"
    }
    }
    ],
    "storeSettings": {
    "type": "AzureBlobFSReadSettings",
    "recursive": true,
    "enablePartitionDiscovery": false
    },
    "formatSettings": {
    "type": "JsonReadSettings"
    }
    },
    "sink": {
    "type": "AzureSqlSink",
    "writeBehavior": "insert",
    "sqlWriterUseTableLock": false,
    "tableOption": "autoCreate",
    "disableMetricsCollection": false
    },
    "enableStaging": false,
    "translator": {
    "type": "TabularTranslator",
    "mappings": [
    {
    "source": {
    "path": "$['taskId']"
    },
    "sink": {
    "name": "taskId",
    "type": "String"
    }
    },
    {
    "source": {
    "path": "$['taskObtainedScore']"
    },
    "sink": {
    "name": "taskObtainedScore",
    "type": "String"
    }
    },
    {
    "source": {
    "path": "$['multiInstance']"
    },
    "sink": {
    "name": "multiInstance",
    "type": "String"
    }
    },
    {
    "source": {
    "path": "$['name']"
    },
    "sink": {
    "name": "name",
    "type": "Int64"
    }
    }
    ],
    "collectionReference": ""
    }
    },
    "inputs": [
    {
    "referenceName": "Json1",
    "type": "DatasetReference"
    }
    ],
    "outputs": [
    {
    "referenceName": "AzureSqlTable1",
    "type": "DatasetReference"
    }
    ]
    }
    ],
    "parameters": {
    "demo": {
    "type": "object",
    "defaultValue": {
    "name": "John",
    "age": 30,
    "isStudent": true
    }
    }
    },
    "annotations": []
    }
}

OUTPUT: