If you receive the following error:
Microsoft.Data.SqlClient.SqlException (0x80131904): Connection Timeout Expired. The timeout period elapsed during the post-login phase
Then this could be because the database you are connecting to is not on a high-enough tier.
When restoring a bacpac to Azure, you can select the tier of the database. Leaving it as standard (s0) results in the database being restored with the following settings:
These are often not enough to do large operations on, such as Obfuscate. Instead, ensure your scaling settings look like this: