A rain sensor just tells you if it’s raining or not. A rain gauge will give you cumulative rainfall values. I know there are DIY projects to make HA-compatible gauges but I’d rather have something out of the box, at least in terms of hardware.
I found this on Amazon, and it appears to be be a clone of a more expensive station by Ambient Weather. It looks like it could be made to work with HA as it has a web interface, but I’m not sure if an app is required for setup. The rain gauge also doesn’t seem super accurate, which is frustrating as that’s the only thing I really care about.
I have the weatherman 2 at my house. It is (unfortunately closed source) a more or less complete weather station, rain sensor (a very good one!), rain gauge, temp, humidity, light sensor, optional wind and wind direction. It involves easy soldering, a little tinkering but its works flawlessly since two or three years in my garden. It is a german project ( http://stall.biz/) no clue if he delivers somewhere else or if the instructions are available in germany. 🤔