SNAP is used in many online services.
I know that the guys from Google Earth Engine are using SNAP (sometimes there are around in this forum).
I’m not sure about Amazon Lambda, but there should be no problem.
it is used in several Thematic Exploitation Platforms, like Urban TEP, Coastal TEP, Polar TEP (not sure). It is used at CODE-DE and ProbaV MEP, etc.
There is definitely no problem in using SNAP for your web service. Actually, we would like to see it.
However, it would be nice if you mention somewhere that you use SNAP and maybe you introduce shortly your service here in the forum when it is running and if it is of interest for a broader audience.
Regarding your question, using SNAPPY or SNAP directly:
I would prefer SNAP for a service. This means that the tech-stack is small. You don’t have python involved. And currently, there are still some issues with the python support in SNAP (which will be addressed soon). However, it means that you have an additional layer which is a source for errors.
But if you want to let users implement parts of your service, e.g. algorithm then Python is probably a got way. But still, you could directly use Java/SNAP directly and just offer a Python interface.