Why is the max_score higher than the _score-sorted first hit's _score in Elasticsearch?

Question

I have an Elasticsearch (8.1) index on which I run a simple match or multi_match query (I tried both, both show the same behavior, even the simplest ones).

In the result it is always the case that max_score is higher than the first hit's _score.

If I add a terms aggregation (on a keyword field) with a top_hits sub-aggregation (with sorting on _score) then the first hit from the first bucket actually has _score == max_score (but it is obviously also a different hit compared to the "main" hits). So, the top_hits aggregation actually does what I want ("fetch all matching documents and sort by _score"). The "main" hits seem to miss some results, however.

How can I make sure that the "main" hits do not "drop" documents? What is the internal mechanics behind this?

I added my PHP array that gets JSON encoded and produces the Elasticsearch query:

[
    'size' => 10,
    'query' => [
        // the result of this does not have all documents
        // that appear in the aggregation
        // and the highest ranked doc has lower score than max_score
        'bool' => [
            'must' => [
                [
                    'match' => [
                        'my_text_field' => [
                            'query' => 'searchword'
                        ]
                    ]
                ],
                ['term' => ['my_other_field' => ['value' => 3]]],
                // plus some more other simple term conditions
                // on other simple integral fields, but no scripts ore similar
                // simple "WHERE a = 5" conditions
            ]
        ]
    ],
    // this aggregation has other/more hits than the directly retrieved docs, matching the max_score
    // If I remove the aggregation nothing changes for the actual result
    'aggs' => [
        'my_agg' => [
            'terms' => ['field' => 'my_agg_field', 'order' => ['score' => 'desc']],
            'aggs' => [
                'score' => ['max' => ['script' => '_score']],
                'filteredHits' => [
                    'top_hits' => [
                        'size' => 10
                    ]
                ]
            ]
        ]
    ]
]