Hotter air holds more water vapor than colder air. For every 1 degree Celsius of warming (how much we've warmed the earth so far on average), the atmosphere can hold about 7% more moisture.

https://www.sierraclub.org/los-padres/blog/2021/08/physics-says-we-re-hot-water

So, yes you are right. As it gets warmer there will be a LOT more water in the atmosphere. This makes for more rain because small changes in temperature can cause huge amounts of water to suddenly "fall out of the sky".