All 3 are correct:
1. "It's rainy again today" is similar to "it's cloudy today", or "it sunny again today" so you're describing the type of weather. Rainy is an adjective, sometimes we also say "it's a rainy day today" which means the same.
2. "It's wet again today" wet is also an adjective that describes the day, so similar to "cloudy" or "rainy" and "sunny". We use this a lot in English when it's raining.
3. "It's raining again today" is a present continuous action, and when it's raining we know that it's also a wet and rainy day. We also use this a lot in English.
So you can use all three. Personally, I would say it's raining again today, or it's wet again today.
Hope this helps!