It doesn't seem to be possible to retrieve the installed firmware version via SNMP.
The closest item I can find is:
snmpwalk -c public -v 2c eaphostname system SNMPv2-MIB::sysDescr.0 = STRING: Linux EAP245 3.3.8 #1 Thu Dec 24 16:06:41 CST 2020 mips
This only provides the Linux kernel version and hardware platform (e.g. uname -srvm), which is not sufficient for determining whether a firmware update is necessary. The only useful information that it provides to the end user is the model number (EAP245).
sysDescr is specified in RFC1213 as:
A textual description of the entity. This value should include the full name and version identification of
the system's hardware type, software operating-system, and networking software.
- replace this string with the installed firmware version ("EAP245 US 220.127.116.11 Build 20201224 Rel. 59228(5553)") ; or
- add the installed firmware version to this string ("Linux EAP245 3.3.8 #1 Thu Dec 24 16:06:41 CST 2020 mips | EAP245 US 5.0.1 Build 20201224 Rel. 59228(5553)"); or
- add the installed firmware version to your private MIB (and publish the OID).
The first option seems best, since the current string provides almost no useful information to the end user.
The second provides reasonable compatibility with any client that uses the current value.
The third provides full compatibility with any existing client, at the expense of requiring use of your private MIB.