Well, your reboot should bring both services back into action, for what it's worth.
If you read this, you'll see that the people who make Raspbian have documented the procedure. To the best of my knowledge this will add the
rpi-eeprom-update command line tool (having installed it in the first line). Additionally, it will add a service which runs it automatically but you can control that as described in the docs. Follow the links in that for more information.
If you do (accidentally) run
rpi-update (bringing in the bleeding-edge
next branch) it WILL automatically update the firmware plus overwrite the EEPROM part of that. If you need to come back from that (bricked Pi) then there's another procedure on there for creating a one-time-use microSD to boot the Pi and bring it the earlier firmware.
The question remains: is the EEPROM update service already in Raspbian Buster Lite from 2019? I had heard that it was. So I'm not sure as to the dating of the documentation. It's possible that this was from around Mar/Apr 2019 (in theory, before they included that). But I don't honestly know.