Unable to upload to azure storage with a SAS Token from flutter

I am attempting to upload files/data to azure storage with a SAS Token. I was successfully able to achieve this without a SAS Token using the following method:

  sendToBlob (Uint8List bytes)async {
    var storage = AzureStorage.parse('DefaultEndpointsProtocol=https;AccountName=#;AccountKey=#==;EndpointSuffix=core.windows.net');
    await storage.putBlob('/test/2.txt',bodyBytes: bytes);
  }

When I generated a SAS Token and took the connection string with it written in the following format, I get a parse error:

"BlobEndpoint=https://#.blob.core.windows.net/;QueueEndpoint=https://#.queue.core.windows.net/;FileEndpoint=https://#.file.core.windows.net/;TableEndpoint=https://#.table.core.windows.net/;SharedAccessSignature=sv=#"

Attempting to send a put request without a connection string, my method is as follows:

  uploadtoAzure(String sas)async{
    try {
      var url = 'https://#.blob.core.windows.net/test/4.txt?'+sas;
      Map<String, String> headers = ({"x-ms-blob-type": "BlockBlob"});
      final response = await http.put(
          url,
          headers: headers,
          body: 'hi'
      );
      print(response.statusCode);
    } on DioError catch (e) {
      if(e.response.statusCode == 404){
        print(e.message);
      }else{
        print(e.message);
      }
    }
  }

Knowing that I'm the Owner and the Storage Blob Data Contributor of the storage account I'm uploading to and the SAS Token is not expired ,this leads to a 403 AuthorizationPermissionMismatch error.

¿<?xml version="1.0" encoding="utf-8"?><Error><Code>AuthorizationPermissionMismatch</Code><Message>This request is not authorized to perform this operation using this permission.
RequestId:bc7f5bb4-c01e-0066-0459-9a6d45000000
Time:2020-10-04T14:16:54.7302685Z</Message></Error>

Is there a method to upload data from flutter to azure using a connection string with a SAS Token? and how would I be able to solve this issue?

Any help is appreciated.