The app is correct, both of those phrases are passive.
Grammatically the passive voice uses the equative verb to be with a past participle of the verb. Both those phrases satisfy that condition.
Semantically, the passive voice involves action being done to the subject. Both those phrases also meet that condition. Rearrange them and you'l see:
[1] "I was exhuasted" --> "${SUBJECT} exhausted me".
The phrase may not seem passive because you've elided the subject, which is part of the problem of the passive voice, it lacks clarity
[2] "Our work here is done" --> "We completed our work"
Like the first phrase, this phrase elides the subject of this sentence, the individuals doing the work. In this case, including the subject ("We") may feel repetitive because of the pronoun "our", but its still more precise.
Also, passive voice isn't bad, however it most often lacks clarity. Sometimes that's okay, and sometimes you want some flexibility with your sentences for effect, such as ending a sentence with the subject (one of the primary reasons to use the passive voice).