

Trans man here, IMHO being nonbinary can be paired with being trans, but not necessarily, i.e. they are not inherently the same thing.
If they have dysphoria and want to transition to alleviate it (irrespective of whether they can), then yes, they are trans.
If the extent of a nonbinary person’s journey is to go by they/them, or they/them + the pronouns associated with their AGAB, then I would not categorise them as trans. To be clear, I am not saying that this is not a valid stance - just that the experience is not the same as being trans, though there may be some overlap.
Obviously you cannot work this out without intimately knowing the person, and it isn’t really anyone else’s business anyway, but to answer the question explicitly, I would refer to them as a nonbinary person (in the absence of further information, and where the ‘nonbinary’ descriptor is relevant otherwise I would just say ‘person’), not a trans person.

That is absolutely wild.
When I was at uni (2016-2019), you had to leave all of your belongings behind in a designated area, and only carry a clear/transparent container with your pen(s) to the exam room. You could optionally bring a clear water bottle (label removed.)
If you ask to use the bathroom, there is no opportunity to go back to your belongings.