Is the question "Are you sober?" asking for whether one drinks alcohol or only whether one recovered from being addicted to alcohol?
This would be dependent on context. The more general case would be checking to see if the person was currently drunk.
And while that question would still apply to a person who previously had an alcohol or drugs problem it would have a secondary meaning in that case, have you started drinking again even if you are not drunk at the moment.
This second usage would require that the two people talking knew each other well enough for this information to be common knowledge between them.
Related question on English.
The one thing it DOESN'T mean is 'do you ever drink alcohol?' That would be 'Are you teetotal?'.
'Are you sober' might refer to a recovery from alcoholism. 'I've been sober now for 3 years!' (Well done!) Or it might simply be asking whether you're currently under the influence of alcohol. 'You're going to drive your car? Are you sure you're sober?'
It's inquiring about their current state.
I would say that "Are you sober" would be an inquiry as to their current state of intoxication (or lack thereof), whether that be the result of alcohol or other drugs. It would basically be the opposite of asking "Are you drunk?" or "Are you high?"
If you wanted to ask about whether someone is maintaining a state of sobriety as a result of recovering from an alcohol or drug addiction, you would instead ask "Are you staying sober?"