Apple released iOS 13.3.1 - some CarPlay implementations were acting up with 13.3. Not sure about Toyota - they didn't release CarPlay for the 2019 Tacoma, they rolled it out on the new RAV4, Camry and Corolla as well as the mid-cycle refresh of the Prius. Toyota says CarPlay and Android Auto will be standard across the line for 2020-2021.
A friend's iPhone isn't playing nice with his JVC I installed, but it works fine with my 11.
In the meanwhile, check to see if a Entune update is available. You can apply those yourself with no need for a Techstream or updater tool. You will need a 4GB or bigger flash drive formated to FAT32 or exFAT to create the updater.