Above comparison of weather sources (providers) indicates a Netatmo/WeeWX driver issue of reporting incorrect rain data (https://github.com/matthewwall/weewx-netatmo/issues/18). This issue of reporting incorrect WeeWX rain summaries for the Netatmo local PWS is solved now.
Thanks to J. Krasinger there exists an updated version of the WeeWX/Netatmo driver. Please have a look at: https://github.com/jkrasinger/weewx-netatmo/. The updated driver code works with Python 2.7 und 3.x (running with versions WeeWX < 4 and WeeWX = 4.x). It can be easily installed by following the given installation instructions. First tests were performed within an existing Raspberry PI setup running WeeWX version 3.9.2. As expected, the WeeWX rain summaries correspond to the Netatmo statistics. At the end of the day the same total amount of rain is displayed on the Netatmo, Weather Underground and WeeWX web interfaces.