Update from me.
Well I took generated destinationContainerUrl and tried to upload by myself the file there. It worked.
Here is a pice of code that I used:
const account = config.storageAccountName;
const sas = config.sasToken;
const blobService = new BlobServiceClient(https://${account}.blob.core.windows.net?${sas}
);
const containerClient = blobService.getContainerClient(config.containerName)
const content = "Hello world!";
const blobName = "newblob" + new Date().getTime();
const blockBlobClient = containerClient.getBlockBlobClient(blobName);
const uploadBlobResponse = await blockBlobClient.upload(content, content.length);
console.log(Upload block blob ${blobName} successfully
, uploadBlobResponse.requestId);
After that I took that https://${account}.blob.core.windows.net?${sas}
URI and just added my container name after a host and it worked!
Hym I don't know exactly what happened :D. Seems that I somehow activated it after a "manual" upload. A bit weird but it is working now :)
Hopefully this info will help someone else