Mysql – Automatically partition a table in thesql (pythesql) everyday for new data

What can I expect performance-wise of such a trigger/partition scheme?

Context switches mean using triggers is always going to use a lot more CPU than a simple insert. The script below can be used to quantify how much impact that will have - and also demonstrates auto-creating partitions using triggers and compares the performance either way.

Please note I haven't included any indexing, or any consideration of update statements.

begin; 
set role dba;
create role stack;
grant stack to dba;
create schema authorization stack;
set role stack;
--
--******** the above creates a nice clean schema as a test area
--
set client_min_messages to warning; --******** or you get a lot of "NOTICE:  merging column "xyz" with inherited definition" notices
--
create table phpheap(log_id serial not null, host text not null, logdate date not null, message text not null); --******** This table is used to compare 'insert' performance with that on the partitioned version
create table php(log_id serial not null, host text not null, logdate date not null, message text not null);
--
create function php_host_insert() returns trigger language plpgsql security definer as $$
begin 
  set search_path to 'stack';
  execute 'insert into php_'||new.host||'_'||to_char(new.logdate, 'YYYYmMM')||'(log_id, host, logdate, message) values($1, $2, $3, $4)' using new.log_id, new.host, new.logdate, new.message;
  return null;
exception when undefined_table then
  execute 'create table php_'||new.host||'_'||to_char(new.logdate, 'YYYYmMM')||'(log_id int not null, host text not null check(host='''||new.host||'''), logdate date not null check(to_char(logdate, ''YYYYmMM'')='''||to_char(new.logdate, 'YYYYmMM')||'''), message text not null) inherits (php_'||new.host||')';
  execute 'insert into php_'||new.host||'_'||to_char(new.logdate, 'YYYYmMM')||'(log_id, host, logdate, message) values($1, $2, $3, $4)' using new.log_id, new.host, new.logdate, new.message;
  return null;
end;$$;
--
create function php_insert() returns trigger language plpgsql security definer as $$
begin 
  set search_path to 'stack';
  execute 'insert into php_'||new.host||'(log_id, host, logdate, message) values($1, $2, $3, $4)' using new.log_id, new.host, new.logdate, new.message;
  return null; 
exception when undefined_table then
  execute 'create table php_'||new.host||'(log_id int not null, host text not null check(host='''||new.host||'''), logdate date not null, message text not null) inherits(php)';
  execute 'create trigger trig_insert_php_'||new.host||' before insert on php_'||new.host||' for each row execute procedure php_host_insert()';
  execute 'insert into php_'||new.host||'(log_id, host, logdate, message) values($1, $2, $3, $4)' using new.log_id, new.host, new.logdate, new.message;
  return null;
end;$$;
--
create trigger trig_insert_php before insert on php for each row execute procedure php_insert();
--
\timing on
insert into phpheap(host, logdate, message) select 'host1', current_date-(generate_series(-99999, 0, 1)/1000)::integer, repeat('hello',20);
--******** output
--INSERT 0 100000
--Time: 1102.140 ms
insert into php(host, logdate, message) select 'host1', current_date-(generate_series(-99999, 0, 1)/1000)::integer, repeat('hello',20);
--******** output
--INSERT 0 0
--Time: 35615.498 ms
insert into php(host, logdate, message) select 'host1', current_date-(generate_series(-99999, 0, 1)/1000)::integer, repeat('hello',20);
--******** output
--INSERT 0 0
--Time: 34074.579 ms
\timing off
--
--******** Now we replace the trigger functions with the 'normal' kind that don't auto-create partitions
--
create or replace function php_host_insert() returns trigger language plpgsql security definer as $$
begin 
  set search_path to 'stack';
  execute 'insert into php_'||new.host||'_'||to_char(new.logdate, 'YYYYmMM')||'(log_id, host, logdate, message) values($1, $2, $3, $4)' using new.log_id, new.host, new.logdate, new.message;
  return null;
end;$$;
--
create or replace function php_insert() returns trigger language plpgsql security definer as $$
begin 
  set search_path to 'stack';
  execute 'insert into php_'||new.host||'(log_id, host, logdate, message) values($1, $2, $3, $4)' using new.log_id, new.host, new.logdate, new.message;
  return null; 
end;$$;
--
\timing on
insert into php(host, logdate, message) select 'host1', current_date-(generate_series(-99999, 0, 1)/1000)::integer, repeat('hello',20);
--******** output
--INSERT 0 0
--Time: 28457.146 ms
\timing off
--
rollback;

Use the first query from the answer you linked and add a simple WHERE clause to get the partitions of a single table:

SELECT
    nmsp_parent.nspname AS parent_schema,
    parent.relname      AS parent,
    nmsp_child.nspname  AS child_schema,
    child.relname       AS child
FROM pg_inherits
    JOIN pg_class parent            ON pg_inherits.inhparent = parent.oid
    JOIN pg_class child             ON pg_inherits.inhrelid   = child.oid
    JOIN pg_namespace nmsp_parent   ON nmsp_parent.oid  = parent.relnamespace
    JOIN pg_namespace nmsp_child    ON nmsp_child.oid   = child.relnamespace
WHERE parent.relname='parent_table_name';