No Apple CarPlay after upgrading to Sync 3.4 – am I missing something?

Hello.

Does a message about incompatible hub appear? Have you tried with android auto?.
Have you performed a master reset?.

Since your vehicle is 2016, you would need to upgrade the USB hub as well.

Take a look at this guide → Media Hub, CarPlay Compatible - 2015-2020 Ford/Lincoln - SYNC 3