Work is underway to add LTI 1.3 support for Moodle as a Tool Consumer (see MDL-62599). The project at https://docs.moodle.org/dev/index.php?title=LTI_1.3_support seeks to scope out the requirements to make similar updates for the LTI Tool Provider functionality in Moodle. It also highlights some issues with the current implementation. If you are using this feature of Moodle your feedback would be appreciated.
Thanks.