Custom progressive sequence (per year) with a column as prefix - postgresql

Question

I need to create a custom sequence based on a specific column, added as a prefix. I know it is possible to customize the sequence as well as the nextval, but I'm not sure if it is possible to use the column of a specific table.
This is the structure of the table with the essential information:
create table tab
(
id serial not null
constraint tab_pkey primary key,
year varchar(4) not null,
seq varchar(20) not null
);
create sequence tab_id_seq as integer;
I would like to automatically populate the "seq" column, as happens for normal sequences, according to this format:
{year}_{sequence}
where {year}_ is the prefix, while {sequence} is a progressive that starts again from 1 every year.
DESIRED RESULT
|--------|----------|---------|
| id | year | seq |
|--------|----------|---------|
| 10 | 2019 | 2019_1 |
|--------|----------|---------|
| 11 | 2019 | 2019_2 |
|--------|----------|---------|
| 12 | 2019 | 2019_3 |
|--------|----------|---------|
| 13 | 2019 | 2019_4 |
|--------|----------|---------|
| 14 | 2020 | 2020_1 | <--- sequence restarting
|--------|----------|---------|
| 15 | 2020 | 2020_2 |
|--------|----------|---------|
| 16 | 2020 | 2020_3 |
|--------|----------|---------|
N.B. there is no direct relationship between the id column and {sequence} element

Answer 1

For the following test structure :
create table test
(
id serial primary key
, year_val int
, seq varchar (10)
);
create or replace function fn_test () returns trigger language plpgsql as $$
declare
res_name varchar;
begin
drop table if exists tmp_test;
create temporary table tmp_test as select * from test;
insert into tmp_test values (new.id, new.year_val);
with cte as
(
select *
, year_val::varchar||'_'||(count(*) over (partition by year_val order by id))::varchar as built_res_name
from tmp_test
)
select built_res_name into res_name
from cte
where id = new.id;
new.seq := res_name;
return new;
end;
$$;
CREATE TRIGGER tg_test BEFORE INSERT ON test
FOR EACH ROW EXECUTE FUNCTION fn_test();
insert into test (year_val)
values (2019),(2019),(2019),(2019),(2020),(2020),(2020);

Answer 2

In the end I found a solution by using multiple sequences (one per year), created dynamically when entering the record.
A trigger, before the insertion invoke a procedure that creates the sequence (if it does not exist) and assigns the value to the seq column (if not assigned).
WORKFLOW
record insertion
sequence creation 'tab_ {year} _seq_id' if it does not exist
if the column seq is empty the value nextval is assigned (tab_ {year} _seq_id)
test insertions and deletions to verify that the column is populated in the correct way
TABLE STRUCTURE
CREATE TABLE tab (
id serial not null constraint tab_pkey primary key,
year varchar(4) not null,
seq varchar(20)
);
FUNCTION
CREATE FUNCTION tab_sequence_trigger_function() RETURNS trigger AS $$
BEGIN
IF NEW.seq IS NULL OR NEW.seq = '''' THEN
EXECUTE ('CREATE SEQUENCE IF NOT EXISTS tab_' || NEW.year || '_id_seq AS INTEGER');
NEW.seq = NEW.year || '_' || nextval('tab_' || NEW.year || '_id_seq');
END IF;
RETURN NEW;
END;
$$ LANGUAGE plpgsql;
TRIGGER
CREATE TRIGGER tab_sequence_trigger
BEFORE INSERT ON tab
FOR EACH ROW
EXECUTE PROCEDURE tab_sequence_trigger_function();
TEST
INSERT INTO tab (year) VALUES (2019);
INSERT INTO tab (year) VALUES (2019);
INSERT INTO tab (year) VALUES (2019);
INSERT INTO tab (year) VALUES (2019);
INSERT INTO tab (year) VALUES (2019);
DELETE FROM tab WHERE id=5;
INSERT INTO tab (year) VALUES (2019);
INSERT INTO tab (year) VALUES (2019);
INSERT INTO tab (year) VALUES (2020);
INSERT INTO tab (year) VALUES (2020);
INSERT INTO tab (year) VALUES (2021);
DELETE FROM tab WHERE id=8;
DELETE FROM tab WHERE id=9;
INSERT INTO tab (year) VALUES (2021);
INSERT INTO tab (year) VALUES (2020);
RESULT
SELECT * FROM tab;
----------------------
| id | year | seq |
----------------------
| 1 | 2019 | 2019_1 |
----------------------
| 2 | 2019 | 2019_2 |
----------------------
| 3 | 2019 | 2019_3 |
----------------------
| 4 | 2019 | 2019_4 |
----------------------
| 6 | 2019 | 2019_6 |
----------------------
| 7 | 2019 | 2019_7 |
----------------------
| 10 | 2021 | 2021_3 |
----------------------
| 11 | 2021 | 2021_4 |
----------------------
| 12 | 2020 | 2020_3 |
----------------------