Older AirPort Extreme 2nd Gen

Not sure why you feel that upgrading the firmware will force you to buy a newer model.

7.8.1 adds some important security updates from 7.6.9, as 7.6.9 did from 7.6.8 and so forth, so unless you have some special needs, you should update the AirPort to pick up the latest security fixes.

Worst case, you can always roll back the firmware to the previous version if 7.6.9 if 7.8.1 does not work out for some unknown or unforeseen reason.

For what its worth, I still have an older 2nd Gen AirPort Extreme here that I use on occasion, and the 7.8.1 update is working just fine.

Although Apple exited the router business in April 2018, they have continued to offer firmware updates for AirPorts that are up to 10 years old.

Your call if you don't want to update the firmware / security of the AirPort.