How use raise notice in nested and sub-function?
Yes it is possible. I have tested the following with PG 12.2 and with psql CLI:

show client_min_messages;
client_min_messages 
---------------------
notice
(1 row) 
create or replace function f2 () returns text
as
$$
declare
begin
 raise notice 'Function 2 is now running';
 return 'f2: OK';
end;
$$
language plpgsql;
CREATE FUNCTION
create or replace function f1 () returns text
as
$$
declare
begin
 raise notice 'Function 1 executing';
 perform f2();
 return 'f1: OK';
end;
$$
language plpgsql;
CREATE FUNCTION
select f1();
psql:t2f.sql:27: NOTICE:  Function 1 executing
psql:t2f.sql:27: NOTICE:  Function 2 is now running
   f1   
--------
 f1: OK
(1 row)