SQL Server 2016 DB Mail Not Sending

I'm on SQL Server 2016 and having a blast... my DB Mail isn't sending and I'm running out of places to look. I double checked the SQL account permissions to the DBmail executable - it has read and execute. I entered a rule for the firewall outbound port 587. I tried another mail account and profile with the same unsent issues. The only entries in the logs (db mail logs) are starting and ending of the service. There are no errors anywhere that I can find. The emails appear to simply enter the send queue and never leave it. The accounts can send and receive email on their own and from a SQL Server 2014 instance on another machine.

I've got a queue of items with sent status "unsent" and checked all the normal places with expected results in all of them, aside from a long queue of unsent mail:

SELECT * FROM msdb..sysmail_event_log order by log_id DESC

SELECT * FROM dbo.sysmail_mailitems

SELECT * FROM dbo.sysmail_sentitems

USE msdb
SELECT sent_status, *
FROM sysmail_allitems

 SELECT is_broker_enabled FROM sys.databases WHERE name = 'msdb';

 EXECUTE msdb.dbo.sysmail_help_status_sp

I have tried turning it off and on again... so did I miss a DMV etc. that could shed light on this situation? Is this a known issue with SQL Server 2016 that I haven't in my searches? Any other possible steps to get this mail sent?

On a whim, when double checking permissions, I double clicked on the actual DB mail executable. The result on the SQL Server 2014 machine was an empty command window. On SQL Server 2016 clicking the DB Mail executable presented this message:

I cannot find this requirement anywhere in the SQL Server 2016 documentation, yet it is clearly a requirement. DB Mail is functioning perfectly with no other changes than installing .NET 3.5.

StackExchange Database Administrators Q#142080, answer score: 17