Terms and their definitions-ish that are pretty broad but may vary by jurisdiction:
Capacity: ability to make a specific decision at a specific time, determined by a physician (or other medical person per state law)
Competence: ability to make all medical decisions from a point in time going forward, determined by a judge
Your patient lacks capacity to make a decision regarding ECT at this time. Have they been determined incompetent per judge and been appointed a guardian?
Emergency: immenent threat to life or life of patient or other
Urgency: moderate potential for the development of emergency without intervention in the near future.
Cataonia is always at least an urgency and may be an emergency if: 1) malignant catatonia or 2) violence emerges (and remember even the most ******ed catatonic person can hit you out of no where, it's happened to me).
Treatment: first line: benzos, ect, restarting clozapine if cataonia emerged during withdrawal. Second life: who knows, some say clozapine, there are a million other things. Always do the first line stuff in emergency, including iv benzos in an icu. If medicine whines, show them uptodate. Benzos or ect are always reasonable alone, unless high dose benzos fail or ect cannot be administered quickly enough in an emergency.
Now, to your question:
Patient with out capacity, has not been court ordered incompetent. First question: mental or not mental health. Some states say the surrogate decision maker doesn't matter in the case of a mental health decision, only courts can mandate treatment (or physician in an emergency). Next question: is there an advanced directive specifying treatment desired in this situation. Again, whether this would be valid in your state for mental health care depends. Next, is this emergency or urgency. You, as a physician, need to know the emergency laws on day one of intern year in your state. Call your attending in a panic now. If it's an urgency, call legal and ask a specific question using the terms above. There also may be specific ect laws, thanks Scientology.
I have worked in places where when a patient lacks capacity, for mental health care physician makes the decision in an emergency and court in any other case and in other places where a POA or NOK matters. In most of the places that I have worked, this person would be brought to court and treated over objection after the judge ruled (and judge would probably order ect only if that was wishes of POA and MD but wouldn't not have to), but if they developed unstable vitals or violence, they would be given lots of benzos until ECT could be stared and then taken to court when safe to continue the benzos and ECT.
Edit: remember, there is a decent chance that there is an underlying medical eitology of the cataonia and the patient can't make a chief complaint, so rule out and treat with a shotgun approach. Treating the underlying cause is also first line.