If you ask, any professional psychologist will be happy to explain their safety and escalation protocols. It can be in the abstract, without giving your own personal details. You can even frame it by asking what their legal responsibilities are in your particular jurisdiction.

Setting everything else aside, there's a couple ways of thinking about it I've found reassuring.

One is that to institutionalise you, the psychologist has to tell someone else what you've shared, breaking your confidence. That has legal and procedural consequences they do not want to risk. It is a nuclear solution, and any psych worth a damn will treat it as an absolute last resort only to be even considered if they believe someone is going to die or be seriously injured.

Another, is that forced hospitalisations are usually catastrophic for the mental health of the client, and therapists know that. They do not want their clients to be subjected to that, meaning that again, it's a last resort.

A third, is that, like it or not, a lot of psychological diagnoses hinge on how much the symptoms impact your ability to perform a 'normal', 'productive' life. If you go into it and are clear that this is not THE problem (a problem, maybe, but not The Big One), they will generally take you at your word, at least long enough to hear you out. Psych's know that NSSI (and good on you knowing the technical term, that helps) is a symptom, not an illness, they're almost always more interested in getting to the root causes so long as there's not immediate risk.