You can configure getRankingInfo for your search. This will provide additional information about rules, etc. that were used as part of the ranking calculation for that query. Note, however, that this will cause an increase in payload size for each request.
You can see the exact additions to the payload (including the relevant pieces for rules) here:
Most useful to you:
Promoted hits are labelled with a "promoted": true field inside the _rankingInfo object. This field is omitted from regular hits.
The list of applied Rules is available inside the appliedRules top-level field. This field is omitted when no Rule has been applied (even if enableRules is true).
The params response field also has search parameters after Rule application, and as such reflects the side-effects of the Rules.