YANBU OP. No matter how much the literal of mind chant "You are harming yourself, therefore it's self-harm, sorry 😊" that's not what the phrase "self-harm" means in practice in the real world.
Outside of some special use cases (e.g. metaphorical usage like "a societal act of cultural self-harm", or the occasional instance of someone using "self-harm" to refer to other harmful acts or habits like overeating or procrastination, in order to make a point), the term "self-harm" is widely understood to refer to a specific type of activity in which somebody deliberately causes themselves physical harm, with the intent of causing harm (and usually without suicidal intent), for a variety of reasons and purposes, but usually in the context of distress caused by mental illness or a history of trauma (or possibly in the context of social contagion). It's often things like deliberate injury to the skin, or sublethal ODs, things with the purpose of causing harm. The intent will generally be to cause damage and/or pain, maybe as a release, a distraction, an externalisation, a rush, a sensation, a punishment, maybe something else. It's complex, but causing harm (and/or pain) is generally the point.
Skin-picking, hair-pulling, nail biting and similar behaviours are completely different. The reasons behind it, the emotions, the nature of the compulsions, the thought processes, the intended outcome, the neurobiology, the most-often-associated mental health or other conditions, the most effective types of treatment, are ALL DIFFERENT from those you see in those types of behaviours that are usually labelled as "self-harm".
Very often, people with these body-focussed repetitive behaviours are following a powerful instinct (one which we share with other animals, which can develop similar difficulties) to remove irregularities or anomalies, in an attempt to heal, not harm. And it feels good to remove things your brain is telling you need removing. People who do these things might be seeking correctness, perfection, a good sensation, satisfaction, focus, or something along those lines. Sometimes their hands and mouths will automatically carry out these behaviours, outside their conscious awareness, in the same way you might jiggle your leg, brush hair out of your eye, or scratch an itch.
The self-injurious behaviours sometimes seen in e.g. some autistic children are different again.
Just because self-harm means "harm to the self" doesn't mean that, in practice, the term is actually used to cover any behaviour that causes harm to the self.
People who read that a person "self-harms" are probably going to proceed on the basis that this person likely cuts or maybe burns themselves, maybe takes ODs, deliberately causing themselves harm with the intent to cause harm, and probably as a maladaptive way of dealing with overwhelming distress.
They're pretty unlikely to think it might mean the person has a compulsion to remove hairs that don't feel like they belong where they are, or that they're in a neverending cycle of feeling compelled to make their fingertips perfect and smooth knowing it's only making it worse even though that's the last thing they want, or that their mouth and/or hands automatically drift to doing that whenever their attention is elsewhere, without realisation that it's occurring, let alone an intention to cause harm.
Using "self-harm" to refer to BFRBs (and SIBs) is misleading and potentially damaging, because a lot of people will interpret it to mean those specific kinds of behaviours (with their associated thoughts, feelings, and intentions) that are normally being referred to when people say "self-harm", and which need completely different management.