Wet insulation will cause drywall to sag between fasteners, then the joints will split and the tape will curl and there will be a mess in the floor every day until it stabilizes.
With a plaster ceiling, the wood laths will get wet, swell, and the plaster will begin popping off. Cracks and splits may run in any direction.
Either way, the best solution is to replace with drywall. BUT, if the cracks and splits are stabilized and not getting worse, no sagging or pieces falling, you may be able to patch it up with drywall joint compound and it may last for several years. But if pieces are falling, it's time for a replacement.
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