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Answering my own question to help others who might face the same issue in the future. While I still don't understand why in some cases the script_score gets called more than once, I was able to fix the scoring.

To prevent the scoring from being summed or multiplied I added boost_mode: replace parameter like below:

{
  "query": {
    "function_score": {
      "query": { ... },
      "boost_mode": "replace", // Adding this fixed the issue for me
    }
}

I found this solution by looking at OpenSearch docs https://opensearch.org/docs/latest/query-dsl/compound/function-score

You can specify how the score computed using all functions[1] is combined with the query score in the boost_mode parameter, which takes one of the following values:

multiply: (Default) Multiply the query score by the function score.

replace: Ignore the query score and use the function score.

sum: Add the query score and the function score.

avg: Average the query score and the function score.

max: Take the greater of the query score and the function score.

min: Take the lesser of the query score and the function score.

[1] Note that the boost_mode works in both scenarios: whether you have a single function (as in my case) or multiple functions (also in case of multiple functions you might want to look at score_mode parameter too from the same docs page that I provided its link above)

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