A word or phrase for "temporarily not working"

You can always say "I will be unavailable (or out of the office) until February 27th with limited ability to check e-mail or voicemail". That is ambiguous in terms of why you're not working, but is still informative.

Maybe one of these simple words: “missing”, “absent”, “away”, “not present” or “off”.

(I think “away” is nice)

Try focusing on location and be vague about it, focusing on where the person is not. You can probably get more specific if you know the party you're talking to and are sure that they aren't creepy.

"out of the office" + a period of time

Mrs. Smith will be out of the office until Tuesday.

"not in today"

Mr. Doe is not in today.

"out of town"

It's perfectly normal to say "I'm off work this afternoon/week/month" if you have a job but you're not actually working at it for some specified period of time (sickness, holiday, etc.).

For longer periods you might say something like taking a sabbatical, or on maternity/paternity leave, which implies your job is being held open until you return.

If you don't have that kind of "permanent position" (you're a freelance actor, for example) it's common to say you're between jobs, but that doesn't seem to apply to OP's circumstances.