Hi Colin,
You would only use the infinitive as a second verb in the same clause but here we only have one verb in each -
être occupé = to be busy
and
se reposer = to rest
which are conjugated.
J'ai été très occupé = I have been/was very busy
Je me suis enfin reposé = I finally rested
So occupé and reposé are past participles.
Let me know if I need to explain further.