This B4A app and its B4J counterpart can be found at https://www.b4x.com/android/forum/threads/tbirdsync-thunderbird-contacts-calendar-tasks-mirroring-from-pc-to-android-sources-included.130715/
Background
I hesitated to post this as it's probably only useful for a small audience (if any), but as I didn't find another solution, perhaps it can benefit others who are looking for this or for something similar.
I've been using the excellent MyPhoneExplorer (https://www.fjsoft.at/en/) for...