I agree with you that the desktop version should allow us to file an online extension, or at least point us to the turbotax online site that allows us to do that. (Unfortunately, I'm not in charge of Turbotax functionality!)
Fortunately, you found and listed the online site for turbotax that allows for filing an extension.
While I have not used it, I believe the IRS also has a site for this at
https://www.irs.gov/forms-pubs/extension-of-time-to-file-your-tax-return
