Seems like no one tested SNMP on ESP32, so I can clarify that SNMP v2 with custom MIB is working OK on ESP32, using LWIP SNMP implementation.
tested with TCP.

Yes. I've solved my problem with SNMP using instructions on LWIP SNMPv2c Agent from LWIP web site.
http://www.nongnu.org/lwip/2_0_x/group__snmp.html
Here is nothing to do with ESP32, You need to deal with LWIP.

Is it possible to use SNMP private MIB ?
Any examples available ?