Learn Hardcore Spanish (Latin America): La copiadora está ocupada; uso la grapadora para unir mis apuntes. - The copier is busy; I use the stapler to bind my notes.

engrapadora / engrapar: Mexico, much of Central America.
abrochadora / abrochar: Argentina, Uruguay, Paraguay.
corchetera / corchetear: Chile.
engrampadora / engrapar: parts of the Andes (e.g., Peru, Bolivia). Use the local term if you want to sound native; otherwise grapadora is generally understood.

Use estar for temporary states and current status. Está ocupada means “it is busy/in use right now.” Using ser (es ocupada) would sound like you’re describing an inherent trait, which doesn’t fit here.

Can ocupada describe a machine, not just a person?

Yes. Ocupado/a commonly describes things that are “in use”:

El baño está ocupado.
La copiadora está ocupada. You can also say: está en uso, la están usando, or no está disponible.

Is the semicolon (;) natural here in Spanish?

Yes. A semicolon can link two related independent clauses. Alternatives that feel very natural in everyday writing/speech:

La copiadora está ocupada, así que uso la grapadora…
La copiadora está ocupada; por eso uso la grapadora… Avoid a simple comma between the two sentences (comma splice).

Why use the simple present uso instead of estoy usando?