I've tested this with both a ESP32-POE-IND and a ESP32-POE-ISO. Both get the same readings from touchRead() but there is no change whatsoever when touching the wire connected to either of the GPIO(13,14 or 15). This is with the example sketch that comes with the ESP32 install.
The other Touch GPIO's do work.
There is no hardware reason for that. GPIO13, GPIPO14, GPIO15 are available. Do you have anything attached to the UEXT that might influence them?
Nothing attached, only to either GPIO13 or GPIO15 in the initial tests. Later tested all the individual pins noticing that GPIO13,14 and 15 don't get any input. Probably something in Arduino/Espressif framework. For compatibility reasons with custom libs I have to use version 3.5.0.
Maybe try to use them as simple GPIO and check if that works.