" These grapes are ripening. They will be ready to pick in about a week. The grapes are firm / mushy / rotten / moldy / dried / crinkled.
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The opposite of soggy in this context would be firm.
Ripe is the adjective, whereas, Ripen is the verb (as already mentioned).
e.g. Those grapes are ripe/A ripe banana (adjective) or Have the grapes ripened yet? (verb, past participle of ripen)
~ Gingernut
I would use "soggy" with soil, sponge, cereal, biscuits, bread or sandwich but never with grapes.