IF (TG_OP = 'INSERT') THEN UPDATE public.companies SET client_code_increment = (client_code_increment + 1) WHERE id = NEW.company_id;
The line above was updating the client_code_increment even if the customer was inserting data by hiimself, which is wrong.
The client_code_increment must be updated IF is an insert AND if the customer did not insert data into the code column.
Correction:
IF (TG_OP = 'INSERT') AND NEW.code IS NULL THEN UPDATE public.companies SET client_code_increment = (client_code_increment + 1) WHERE id = NEW.company_id;