Given the json structure in the link, we can obtain linear results with associative arrays, as the comments suggested. I assume you will load the JSON once and then perform many queries on the data:

<?php
$data = json_decode( file_get_contents( 'ingredients-dataset.json' ), true );

$interactions = [
    "affected_by" => [],
    "binds" => [],
];

// Walking the JSON structure
foreach ( $data['categories'] as $category ) {
    foreach( $category['pages'] as $page ) {
        // Preventing warnings
        if ( !array_key_exists( 'interactions', $page ) ) {
            continue;
        }
        // Note the reference &
        foreach( $interactions as $action => &$action_array ) {
            if ( !array_key_exists( $action, $page["interactions"] ) ) {
                continue;
            }
            foreach( $page['interactions'][$action] as $interactant ) {
                // Create new empty array, if it doesn't exist already
                if ( !isset( $action_array[$interactant] ) ) {
                    $action_array[$interactant] = [];
                }
                // Add to said array
                $action_array[$interactant][] = $page["id"];
            }
        }
    }
}
// Print the results
echo "affected_by hard-water: "
    .implode( ", ", $interactions["affected_by"]["hard-water"] )
    ."<br>";

echo "binds to calcium-ions: "
    .implode( ", ", $interactions["binds"]["calcium-ions"] )
    ."<br>";

Result:

affected_by hard-water: coconut-oil, aqua
binds to calcium-ions: etidronic-acid, tetrasodium-edta