Need help with Store-API CMS endpoint

We are using a plugin which adds a downloads block to the page. The data returned only includes the media id and we need the media information to included.

We’re using this store-api endpoint:
/store-api/cms/{PAGE__UUID}

{
    "blocks": [
        {
            "versionId": "0fa91ce3e96a4bc2be4bd9ce752c3425",
            "type": "na15-downloadcenter",
            "slots": [
                {
                    "versionId": "0fa91ce3e96a4bc2be4bd9ce752c3425",
                    "translated": {
                        "config": {
                            "category": {
                                "value": "018baf2b4117742d9d52e3f1563d2a32",
                                "source": "static"
                            }
                        },
                        "customFields": {}
                    },
                    "createdAt": "2023-11-22T13:32:22.129+00:00",
                    "updatedAt": "2023-12-04T10:58:37.719+00:00",
                    "type": "na15-downloadcenter",
                    "slot": "content",
                    "block": null,
                    "blockId": "018bf73b3bc970938bf24824406cd089",
                    "config": {
                        "category": {
                            "value": "018baf2b4117742d9d52e3f1563d2a32",
                            "source": "static"
                        }
                    },
                    "fieldConfig": [
                        {
                            "name": "category",
                            "source": "static",
                            "value": "018baf2b4117742d9d52e3f1563d2a32",
                            "apiAlias": "cms_data_resolver_field_config"
                        }
                    ],
                    "translations": null,
                    "data": {
                        "_uniqueIdentifier": "018c399b9c2071ba8f98cfa10d64a935",
                        "translated": [],
                        "files": {
                            "018baf2b825f7b6b97931ea1cb41d409": {
                                "translated": {
                                    "title": "Test download",
                                    "mediaId": "018badc8d503753eb48ad6704da76b0f"
                                },
                                "createdAt": "2023-11-08T13:43:35.725+00:00",
                                "updatedAt": "2023-12-04T14:06:20.317+00:00",
                                "category": {
                                    "translated": {
                                        "title": "Test category"
                                    },
                                    "createdAt": "2023-11-08T13:42:14.981+00:00",
                                    "updatedAt": null,
                                    "id": "018baf2b4117742d9d52e3f1563d2a32",
                                    "title": null,
                                    "apiAlias": "na15_file_category"
                                },
                                "priority": null,
                                "id": "018baf2b825f7b6b97931ea1cb41d409",
                                "title": null,
                                "mediaId": null,
                                "apiAlias": "na15_file"
                            }
                        },
                    },
                    "apiAlias": "cms_slot"
                }
            ],
        }
    ]
}

For the product endpoint I ended up using this in order to include media entity data:
store-api/product/{PRODUCT__UUID}

{
    "associations": {
        "na15_file": {
            "associations": {
                "translations": {
                    "associations": {
                        "media": {}
                    }
                }
            }
        }
    }
}

Is something like this possible for the CMS endpoint as well? Or is there a way using the store-api we can retrieve media information by id?