Extended statistics for correlated columns, row estimates when values are not in MCVs list

On version 12.5, I have a query similar to the below where I am getting
rather unfortunate row estimates and a sub-optimal index choice as a result.

SELECT
id
FROM
messages
WHERE
client_id = 1234
and site_id = 889977
and message_type_id in ( 59, 62, 102, 162 )
and sent_on > NOW() - INTERVAL '3 days';

I created extended statistics (all types) on client_id and site_id,
analyzed the columns, and in pg_stats_ext.dependencies (4 = client_id, 7 =
site_id) have:
{"4 => 7": 0.002997, "7 => 4": 0.896230}

When I check row estimates like below, I get results that indicate the
columns are expected to be independent still.
explain SELECT id FROM messages; --889594304
explain SELECT id FROM messages where client_id = 1234; --133439
explain SELECT id FROM messages where site_id = 889977; --28800
explain SELECT id FROM messages where client_id = 1234 and site_id =
889977; --4

However, I pick a client & site ID pair which show up in the MCVs list,
then I get the same estimate when querying for that site_id with or without
including the client_id. That is great.

Is it reasonable to expect that if the correlation between two columns is
rather high, then the optimizer might figure the columns are not
independent and perhaps would give less weight to the value derived from
independent column statistics? With table statistics, it is possible to set
a static value or ratio for something like ndistinct. Any chance for
something similar on dependency someday?

Perhaps I am expecting too much or have a poor understanding of what
extended statistics can or someday might do. I deal with under estimates
from correlations between client_id and sites or other similar
dependent objects a fair bit and am hopeful to resolve some of those
planning problems with extended stats, without the maintenance overhead of
migrating everything to a single client per database to get more specific
statistics.