Obtain a "list" of stored procedures which include INSERTs without naming the columns involved
There is a DMV called sys.dm_sql_referenced_entities. It returns a column is_insert_all documented thus


  1 = The object is used in an INSERT statement without a column list (object-level only).


This seems to be what you're looking for.

Here's an example of it in practice. First we'll create a simple one-column table

drop table if exists dbo.T1;
go
create table dbo.T1(c int);


Now two stored procedures, one references columns explicitly the other does not.

create or alter procedure dbo.p_named
as
begin
    insert dbo.T1(c)  -- columns are listed
    select 1;
end
go

create or alter procedure dbo.p_not_named
as
begin
    insert dbo.T1   -- no column list
    select 2;
end
go


The DMV is a table-valued function. As such it can be invoked using the CROSS APPLY syntax. The names of procedures to pass to this function can be obtained from the catalog view sys.procedures. The documentation for this DMV states


  schema_name is required when the referencing class is OBJECT.


We can get the schema name using a built-in metadata function handily called SCHEMA_NAME(). Putting it all together we get

select
    p.name, is_insert_all -- other columns exist
from sys.procedures as p
cross apply sys.dm_sql_referenced_entities(CONCAT(SCHEMA_NAME(p.schema_id), '.', p.name), 'OBJECT');


Which returns this

name          is_insert_all
------------- -------------
p_named       0
p_named       0
p_not_named   1