linux has multiple ways of doing things. That link gives two.

It can be confusing!

Unfortunately, that link also assumes homebridge was installed in a particular way. I don't know how you installed yours.

If you installed it differently, you may need to tweak things. Perhaps just the user if you installed homebridge as yourself and not as a new 'homebridge' user on the pi. It should be obvious where/how to edit the two files. :-(

Sorry, people don't do things consistently in Linux, and there's always "a new, better" way. It means lots of customization and frustration, unfortunately.

The absolute simplest way to have homebridge start at boot automatically is to run 'crontab -e' which should open an editor with an empty file.

Create a single line (or add a line if there is stuff there already) (Don't indent it like below. the @reboot starts in the far left column)

@reboot   homebridge

Then save the file and exit out of the editor. Reboot.

You can google crontab - it can be used to run command(s) at specific time(s), and there is a special keyword '@reboot' which can be used to give a command to run at boot time.

Like I said - many ways to skin a cat.

The method given in my prior link is better because it allows you to stop/start/restart homebridge. The @reboot method doesn't give an easy way to stop homebridge or restart it without rebooting the entire pi.