Dissolve with water and add HCL. If gas that can make clear lime water turbid is produced, it means that sodium hydroxide has deteriorated.

But you're missing something. You can't prove whether sodium hydroxide is completely deteriorated or partially deteriorated. You can only prove whether it contains sodium carbonate.

I'll tell you what I know.

Dissolve in water, add phenolphthalein and excess calcium chloride.

If there is precipitation, phenolphthalein becomes colorless, and everything goes bad.

If there is precipitation, phenolphthalein is still red, indicating local deterioration.

If there is no precipitation and phenolphthalein is red, there is no deterioration.