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 also have an ecowitt weather station, bought a separate GW1000 receiver which feeds into weewx (completely local) and home assistant. You can also add in up to 8 extra temp and humidity sensors so I have some of those in different rooms and the green house.
The rain measurement is a tipping seesaw type so strong winds can sometimes cause inaccurate results
Edit: https://www.ecowitt.com/shop/goodsDetail/16
Has usb connector too