It wouldn't have to be deemed a punishment, merely a procedural item as part of establishing the Republic of Britain and eradicating any trace of royal privilege.
> Technically just abolishing the monarchy / taking away their powers would suffice.
It wouldn't suffice, because they still derive a great deal of power from their inherited wealth. What's the point of abolishing the monarchy if we permit them to remain as landlords for huge swathes of the country? Then they're still lording it over people economically, even if no longer doing so constitutionally.
I hope you'll excuse me for phrasing it this way, but it would not be a punishment only because a punishment is a lawful injury, and your "Republic Act" is decidedly unlawful: by interfering with the royals' persons, property, privacy, &c, without any clear finding of wrong-doing on their part, the act is offensive to the common law, the ECHR law, and other fancy international law. (Good legal scholarship has shown us in recent years that most of the ideas in the ECHR and other international conventions are derived from the English common law, a rich tradition of which you should be proud.)
I am no fan of the royals and other nobles and look forward to the day when they all work for a living and wear seat belts like regular people. Yet, we must acknowledge that rule of law means law for the bad, the useless, and the rich. The ends don't justify the means.
> Technically just abolishing the monarchy / taking away their powers would suffice.
It wouldn't suffice, because they still derive a great deal of power from their inherited wealth. What's the point of abolishing the monarchy if we permit them to remain as landlords for huge swathes of the country? Then they're still lording it over people economically, even if no longer doing so constitutionally.