When will the Form 8936 / Electric Vehicle Credit module be ready? The IRS form for 2019 has been finalized and posted to the IRS website.

It will be available on 2/12/2020.  See IRS forms

The fact that the forms are available on the IRS website has nothing to do with any tax software program.  The forms are available if you are going to download from the IRS to complete it on your own.  However, e-filing is different.  Once the form is finalized by the IRS, it has to be coded into the special language the software uses and has to be thoroughly tested for calculations and e-filing acceptability.  IRS then has to approve it for e-file.  It always takes a little longer for a form to become available for e-file in a software program.  I hope this helps you understand the situation.  At this point, the IRS expects to approve the form 8936 on TurboTax e-file as  02/12/2020.  I truly understand your frustration and thank you for your patience.

I filed on feb 13th and was rejected.  As of today, February 20th it says it was updated on 
February 14th. Is it now good to file?

The fix for Form 8936 was included in today's release.  As insurance, delete Form 8936 and reenter it.  It should go through then.