Complicated column dependencies in postgreSQL

I have two columns: column1 with two distinct values (0, 1) and column2 with 3 distinct values ('A', 'B', 'C'). Value in column1 is always 0 for 'A' and 'B' in column2, but if the value in column2 is 'C' then column1 has the next distribution: (0: 15%, 1: 85%). But I have another column departmentid. In some departments distribution of column1 in case column2 = 'C' is (0: 0%, 1: 100%). So in some cases when I have a query

SELECT * FROM mytable WHERE departmenid = 42 AND column2 = 'C' AND column1 = 0 ORDER BY id LIMIT 10;

PostgreSQL chooses to index scan by id and assumes there will be ~25000 rows, but in the table, there are no rows with this filter. So the query scans the whole table by index scan and it takes too long. If db selects bitmap scan it will be 50x times faster (based on other queries on this table). Indexes on all these columns are present.

I have two questions:

1. I created the statistic object on column1, column2 and departmentid, but there are no two interesting to me dependencies: from column2 to column1 and from column2, departmenid to column1. Why? In the statistic object on column1 and column2 dependencies are null. Of course I made analyze.
2. How can I speed up this query? Is there any way to speed up this query without creating a specific 4-column index (departmenid, column2, column1, id)? Because there are a lot of other filters and different orders in real production query (the problem reproduces with this minimal query).

PostgreSQL 16.1, auto -vacuum and -analyze every day, ~3 million rows in the table

update: table definition (it has more than 100 columns and more than 50 indexes, show only related):

CREATE TABLE mytable
(
  id           SERIAL
    PRIMARY KEY,
  column1      INTEGER DEFAULT 0 NOT NULL,
  column2      TEXT              NOT NULL,
  departmentid INTEGER
);
CREATE INDEX mytable_departmentid_index
    ON mytable (departmentid);
CREATE INDEX mytable_column1_index
    ON mytable (column1);
CREATE INDEX mytable_column2_index
    ON mytable (column2);

-- tested statistic
CREATE STATISTICS mytable_column2_column1 ON column2, column1 FROM mytable;
CREATE STATISTICS mytable_departmentid_column1_column2 ON departmentid, column1, column2 FROM mytable;

departmentid - has < 0.0002% nulls, statistic says there are no nulls. Index on id exist due to id is primary key. All indexes are btree.

query plan (other columns are removed, numbers are actual):

Limit  (cost=0.68..501.79 rows=10 width=2690) (actual time=35351.049..47175.738 rows=1 loops=1)
  Output: id, column1, column2, departmentid
  Buffers: shared hit=1682274 read=1646793 dirtied=1640 written=980
  I/O Timings: shared/local read=39193.882 write=9.565
  WAL: records=1637 fpi=1637 bytes=3034199
  ->  Index Scan using mytable_pkey on public.mytable  (cost=0.68..1392081.41 rows=27780 width=2690) (actual time=35351.048..47175.735 rows=1 loops=1)
        Output: id, column1, column2, departmentid
        Filter: ((mytable.departmentid = 42) AND (mytable.column2 = 'C'::text) AND (mytable.column1 = 0))
        Rows Removed by Filter: 3536431
        Buffers: shared hit=1682274 read=1646793 dirtied=1640 written=980
        I/O Timings: shared/local read=39193.882 write=9.565
        WAL: records=1637 fpi=1637 bytes=3034199
Settings: effective_cache_size = '8008368kB', effective_io_concurrency = '0', geqo_effort = '10', jit = 'off', random_page_cost = '1.2', search_path = 'public'
Planning Time: 0.503 ms
Execution Time: 47175.783 ms

update 2: Question 1 has my mistake, there is column2, departmenid to column1 dependency, but no column2 to column1. And also I was wrong that column1 is always 0 for column2 in ('A','B'). Correct information is present in statistic, but that is not a big percent

Why the 4-column index is bad: The end user can select a column to order, so the index will just cover the default case. Filtering by column1 and column2 is also the default. So I prefer to find a more general solution

Question 3: Maybe there is some way to fix this by changing the DDL?

Question 4: Is there a way to calculate dependencies between value to get it by query? Like corr() function.

Information from pg_stats_ext (replaced all attribute number with name):

Information from pg_stats: