I've installed openSUSE Leap 15.4 seeing that it has net-snmp package >= 5.8
assuming it has support for SHA256 and AES256.

My assumptions were only partially correct, namely it has SHA256 authentication
but it doesn't have AES256 privacy protocol.

=========================================================
#~ snmpget -h 2>&1 | grep PROTOCOL
  -a PROTOCOL           set authentication protocol
(MD5|SHA|SHA-224|SHA-256|SHA-384|SHA-512)
  -x PROTOCOL           set privacy protocol (DES|AES)
#~ rpm -qf `which snmpget`
net-snmp-5.9.3-150300.15.3.1.x86_64
#~ snmpget --version
NET-SNMP version: 5.9.3
#~
#~ cat /etc/os-release | grep -iwE "name|version"
NAME="openSUSE Leap"
VERSION="15.4"
#~
=========================================================

I've tested on other systems (Ubuntu) and for a similar version of package that
support is enabled.

=========================================================
#~ snmpget -h 2>&1 | grep PROTOCOL
  -a PROTOCOL           set authentication protocol
(MD5|SHA|SHA-224|SHA-256|SHA-384|SHA-512)
  -x PROTOCOL           set privacy protocol (DES|AES|AES-192|AES-256)
#~ snmpget --version
NET-SNMP version: 5.9.1
#~ cat /etc/os-release | grep -iwE "name|version"
NAME="Ubuntu"
VERSION="22.04.1 LTS (Jammy Jellyfish)"
#~
=========================================================

If I can help with anything else or contribute just let me know and I will try
my best.