I found this thread about problem Auto Mode in the TPS23861PW: https://e2e.ti.com/support/power-management-group/power-management/f/power-management-forum/1191159/tps23861-detection-and-classification-of-poe-pd-not-executed-in-auto-mode/4529754?tisearch=e2e-sitesearch&keymatch=TPS23861#4529754
I have exactly the same problem. After a lot tests I found problem with the SHTDWN pin (No. 24). On all shematics applications this pin is connected to the VDD for each work mode.
I made project with this connection.
Sample units purcharsed from european distribution are working ok, but one spool we purcharsed in China. Chips purcharsed in Chin don't want to work with suggested connection of the SHTDWN pin. If this pin is disconnected (float mode) or connected to the GND classification does start with Auto Mode. I have one chinese LAN switch with the same chip and there SHTDWN pin is connected to the GND over 4k7 resistor.
Could you explain please what's going on?