You can set it as follows,
await blobClient.UploadAsync(stream, true, default);
await blobClient.SetHttpHeadersAsync(new BlobHttpHeaders
{
ContentType = contentType
});
EDIT: As mentioned in the comment, the efficient way to do the same with a single method as follows,
await blobClient.UploadAsync(ms, new BlobHttpHeaders{ ContentType = "text/plain"});
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