Gatekeeping as I’m using it in this context is the act of unnecessarily excluding someone from a community or diminishing their attempts to participate*. That’s why I think the best definition of most personal identity terms is a permissive one, eg. “anyone who decides to transition is trans”. But opening up that definition means we need another way to refer to people who are physically transitioning, because there are meaningful differences in their experiences and needs. (“Physically transitioning” honestly suits this purpose fine IMO.)
But there’s nothing wrong with choosing a narrower definition if you don’t use that to discriminate or exclude non-physically-transitioning trans people from spaces that could apply to them. It’s not a good idea because that message is easily able to be twisted to be exclusionary, but there’s nothing inherently gatekeeping about it; the term that would be common use would likely just become the one that refers to all types of trans people. Defining “trans” to be narrower than the wider definition is only wrong because we’re attached to the current definition. Which is a very good reason to keep that word defined as the broader group, but again someone who isn’t familiar with this would rightly see it as a valid definition.
note that the precise definition matters here, as I believe it does with a great many things