I found out my answer and it's extremely simple. There's a method for it specifically in com.mongodb.client.model.search.ShouldCompoundSearchOperator.class

Bson searchStage = Aggregates.search(
     SearchOperator.compound()
        .filter(List.of(filterClause))
        .should(List.of(SearchOperator.of(searchQuery), SearchOperator.of(searchQuery1)))
        .minimumShouldMatch(1),
        searchOptions().option("scoreDetails", true).option("index", "default")