Better even that the punishment should fit the crime, ie
the perpetrators have to undergo what they made the
victim undergo, in addition to community service.

Except tenfold. Ten buckets on each of their heads of
the foulest sewage available. Public humiliation of some
kind, such that their crime is visible to all. I agree
that a stern talking to or wag of the finger is pointless.

But how do you make someone understand what they
have done? Such that they truly understand, and feel
authentic regret?

Punishment rarely is effective in that regard. It just makes
people better at hiding their crimes. Liars become better
liars. The potential for rehabilitation has to compete with
the natural urge to retaliate against the one who punishes,
or authority in general.

The punished don't usually learn how it feels to be their
victim. That's what's needed, for them to know how it
feels.