If you aren't modifying the ElasticSearch source code, then you don't need to care about any of this conversation at all.
If you add search to your webapp using ElasticSearch, you typically would not be modifying it, and so any source distribution burden that could possibly be compelled from you in a worst-case scenario would be for the unmodified source code that you freely downloaded from a public website. No local modifications? No violation of terms. End of line.
While that's a slight risk of having more burden than not having to provide that source code, it's not like it contains anything proprietary, because you probably aren't modifying it anyways — and once you divulge that source, it's proof that you not only did not violate terms, but could even request legal fees.
So whether or not this search usage would qualify, which can only be definitively decided in a court of law, your actual risk of harm and exposure is none whatsoever — unless you have proprietary patches to ElasticSearch and you aren't already sharing them openly in a GitHub fork. (I'm not your lawyer, etc.)
If you add search to your webapp using ElasticSearch, you typically would not be modifying it, and so any source distribution burden that could possibly be compelled from you in a worst-case scenario would be for the unmodified source code that you freely downloaded from a public website. No local modifications? No violation of terms. End of line.
While that's a slight risk of having more burden than not having to provide that source code, it's not like it contains anything proprietary, because you probably aren't modifying it anyways — and once you divulge that source, it's proof that you not only did not violate terms, but could even request legal fees.
So whether or not this search usage would qualify, which can only be definitively decided in a court of law, your actual risk of harm and exposure is none whatsoever — unless you have proprietary patches to ElasticSearch and you aren't already sharing them openly in a GitHub fork. (I'm not your lawyer, etc.)