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To fully align with CLI output, we might need to also consider omap usage and rounding method differences:
CLI implementation: https://github.com/ceph/ceph/blob/e6fccf6f381e37b38956f3efc33f5c4938a663e1/src/mon/PGMap.cc#L914-L926

Just explored the ceph-mgr API with this and found:

# ceph mgr cli --help

 Monitor commands: 
 =================
...
mgr cli get <data_name>                                                Called by the plugin to fetch named cluster-wide objects from ceph-mgr.
                                                                        :param str data_name: Valid things to fetch are osd_crush_map_text, 
                                                                        osd_map, osd_map_tree, osd_map_crush, config, mon_map, fs_map, osd_
                                                                        metadata, pg_summary, io_rate, pg_dump, df, osd_stats, health, mon_
                                                                        status, devices, device <devid>, pg_stats, pool_stats, pg_ready, osd_
                                                                        ping_times. Note: All these structures have their own JSON 
                                                                        representations: experiment or look at the C++ ``dump()`` methods to 
                                                                        learn about the

It provides an in-memory cached get('df') command, whose output is:

{
    "pools": [
        {
            "id": 1,
            "name": "device_health_metrics",
            "stats": {
                "bytes_used": 0,
                "compress_bytes_used": 0,
                "compress_under_bytes": 0,
                "data_bytes_used": 0,
                "dirty": 0,
                "kb_used": 0,
                "max_avail": 105215721472,
                "objects": 0,
                "omap_bytes_used": 0,
                "percent_used": 0.0,
                "quota_bytes": 0,
                "quota_objects": 0,
                "rd": 0,
                "rd_bytes": 0,
                "stored": 0,
                "stored_data": 0,
                "stored_omap": 0,
                "stored_raw": 0,
                "wr": 0,
                "wr_bytes": 0
            }
        },
        {
            "id": 2,
            "name": "rbd-pool",
            "stats": {
                "bytes_used": 0,
                "compress_bytes_used": 0,
                "compress_under_bytes": 0,
                "data_bytes_used": 0,
                "dirty": 0,
                "kb_used": 0,
                "max_avail": 105215721472,
                "objects": 0,
                "omap_bytes_used": 0,
                "percent_used": 0.0,
                "quota_bytes": 0,
                "quota_objects": 0,
                "rd": 0,
                "rd_bytes": 0,
                "stored": 0,
                "stored_data": 0,
                "stored_omap": 0,
                "stored_raw": 0,
                "wr": 0,
                "wr_bytes": 0
            }
        }
    ],
...
}

'percent_used' is the exact calculation we're looking for.