Is it legal to sign a “contract” like that of Colleen Stan to
voluntarily bond oneself into slavery?
In the United States, this is prohibited by the 13th Amendment to the U.S. Constitution (which also prohibits indentured servitude that unlike slavery was historically often entered into voluntarily in the colonial era in North America).
The 13th Amendment contains an exception for punishment for a crime (which a few states have foreclosed in their own state constitutions). But that isn't applicable in the context of the question, and no U.S. jurisdiction currently authorizes that punishment for any crime, although some involuntary servitude (i.e. "chain gangs") are permitted in some U.S. states for incarcerated prisoners, including people detained in the military justice system where a term for a limited number of years of involuntary "hard labor" is a common punishment for many serious offenses.
In addition to being a crime, any such contract would void ab initio as contrary to public policy and would have no legal effect.
Every country in the world other than the U.S., except not widely internationally recognized ISIS-controlled enclaves, also expressly bans slavery by statute, treaty, or a constitutional provision (some only recently), at least de jure, although de facto slavery persists illegally in a few places.
Similar Circumstances That Aren't Slavery
Military or Paramilitary Service
The closest thing in the U.S. to a legally recognized, voluntary, commitment to involuntary servitude is an enlistment for a fixed term of years in military service (or a handful of comparable civilian but paramilitary service arrangements such as certain positions with the Center for Disease Control). These are the only occupations which you cannot quit at-will subject to only economic sanctions, and for which you can be ordered to undertake tasks that may put you at grave risk of being killed in circumstances that make this necessary arise.
But, the law does not consider military service to be a form of involuntary servitude for 13th Amendment purposes, and military service commitments are never for more than a term of years (typically five years at a time or less).
Also, unlike slavery, military service is not unpaid and leaves the person in military service with some liberties (e.g. the right to marry and the right to practice a religion of your choice), even though other rights of people in military service are limited. Military service also binds you to an organization that is part of a country, not to the service of a single, predetermined individual.
A Guilty Plea To A Serious Crime
One can also voluntarily plead guilty to a crime with a life sentence or a long period of incarceration in excess of one's life expectancy if a prosecutor has charged you with a crime.
Voluntary Commitment To An Institution
One can be voluntarily be committed to a mental institution if the mental institution determines that you are suffering from certain kinds of serious mental impairments or substance abuse.
Adult Guardianship And Conservatorship
One can voluntarily consent to an adult guardianship and/or conservatorship which entails an immense deprivation of liberty and loss of control of your money, but which is only legal for a court to impose if it believes you are incapacitated to a requisite extent or suffer from a serious drug or alcohol addiction.
This kind of relationship, unlike slavery, places the guardian or conservator with a fiduciary duty to act in your best interests, rather than the interests of the guardian or conservator. But if this fiduciary abuses that power, it can be hard for the protected person to obtain relief for the fiduciary's misconduct as a practical matter. There are recent high profile examples of these arrangements being abused.
The only jurisdictions in the world that completely prohibit divorce are the Philippines (for non-Muslims) and Vatican City. Vatican City has very few residents and almost no married residents anyway. The Philippines does recognize the concept of a "legal separation", however, and recognizes divorce for Muslims (and possibly for certain indigenous peoples of this country).
Marriage, obviously, isn't slavery, but has historically greatly limited the rights of married women. These days, only the rights of marriage and sexual freedom are likely to be limited in some jurisdictions by marriage, although legal economic rights are modified by marriage.