There is probably not a universal equation. I think generally extrajudicial killings are immoral in a way that is different from state sanctioned killings, although no state execution is necessarily moral.

If your state is run by a death cult it may be that legal and “legitimate” executions are done out of classist, racist, imperialist intentions. It is probably not controversial to say, without nuance, none of these can be moral.

Extrajudicial killings can delegitimize the state because theoretically it should be able to either execute legally, create a legal means, or, if such laws exist, be able to enforce the law forbidding executions/murder. If a state is oppressing the capitalist class via executions, it must do so openly and legally. If a state is opting to not deal out executions, it should find means of legal force. Otherwise, it proves itself untrustworthy, or unable to carry out its mandate.

I suppose there could be exceptions to this where the state needs plausible deniability among the (imperialist) international community. It’s hard to imagine something legal not being at least somewhat public, but maybe it could be done legally and secretly. I think resorting to this is ultimately a dangerous path to go down. Nobody needs a purge to get out of hand, it helps no one.

In the early 19th century, the Cherokee outlawed any sale of land by Cherokee people to the US under penalty of death. However, the state would not directly carry out executions. Instead, the state revoked any and all protections from the perpetrator, meaning any and all of the perpetrators’ compatriots were basically allowed to kill them at any point, essentially booting them from the nation and the states jurisdiction.

In this case we have sanctioned killings that are not carried out by legally designated, professional court authorities but rather anyone that is willing and able. The state is more nebulous in this situation. It is still the “state” in a very broad sense that is executing them because it is enabling anyone to do it for them which differs from Anglo/Western legalisms. But it is not like the court sentences anyone to die on a certain date and then enforces it to be done by a sanctioned official. There are not really any police to hunt down perpetrators, only community members to jump them. These indirect executions killings, where anyone can kill you if the state wills it, are probably more moral than an unsanctioned murder done by a state agent because the victim is legally ignored by the state in the popular interests of survival and maintains its legitimacy.

During this period the state of Georgia sought to undermine the Cherokee Republic by outlawing Cherokee laws, among other things, in an effort to make their lives as miserable as possible so they would agree to sell their land and leave. So here is an example of perhaps needing to take care of things inconspicuously, with some plausible deniability to perhaps confuse the settler states. In this case, if the Cherokee did something reasonably extrajudicial as a means of carrying out the spirit of the law designed to ensure survival, it would not necessarily be immoral, because there are unique circumstances.