Lua: how to read .INI (text format) file only even lines and keeping only the right-side of a line after specific character

I'm not a LUA programmer but sometimes I have to deal with.

Please here my issue:

I have an .INI file that's a text simple text formatted file, in which each setting is written in 2 lines in this way (here below the format used):

[machine_readable_plugin_name]
(plugin_name.maker.tld),flag=0|Human Readable Plugin Name (Maker)

The file contains hundreds of couple of lines like the one here above.

For each couple of lines, I need to:
Avoid all the first lines that are containing the "[]", I don't need their content
And from the second line, get only what is coming after the Pipe character "|"

print(string.match(s, "|(.*)"))

Returns me an empty string.
"s" contains the file's line I'm reading it by a "FOR END" cycle in which the above line code is in it.
By using print(s) I got all the lines printed out

What I need, is to get for each couple of line, the print() should return

Human Readable Plugin Name (Maker)

So, if the .INI contains 20 lines, I need to get 10 times

Human Readable Plugin 1 Name (Maker 1)
Human Readable Plugin 2 Name (Maker 2)
Human Readable Plugin 3 Name (Maker 3)
...
...
Human Readable Plugin 10 Name (Maker 10)

NOTE: the .INI file is not made by me. It's with the application and I can't modify it's format. It is what it is.

EDIT 1

Please here the code you kindly asked into the comments

local path_ = 'K:/APP_NAME/settings-win64.ini'
local handle_ = io.open(path_, "r")

for _ in handle_:lines() do
    s = handle_:read("*l")
    print(s) -- this output is ok. All lines are printed

    if _ == nil then 
        handle_:close() 
      else
     
        if s ~= nil then 
          human_Name = string.match(s, "|(.+)$")
          print("TEST") -- this one is printed out as expected.
          print(s) -- this one is printed out as expected.
          print(human_Name) -- this one is empty. Nothing is printed.
        end
    end -- if 1
  end -- for

All anomalies were generated within this couple of lines:

for _ in handle_:lines() do
    s = handle_:read("*l") <--- this line was the main issue generator

LUA was reading the file and it was reading it 2 times, creating all the issues I faced-out.

By removing the the second line, and modifying the code accordingly, everything started working fine. Also with the test file published by @Oka in the comments here below

local path_ = 'K:/APP_NAME/settings-win64.ini'
local handle_ = io.open(path_, "r")

for _ in handle_:lines() do
    --s = handle_:read("*l")
    print(_) -- this output is ok. All lines are printed

    if _ == nil then 
        handle_:close() 
      else
     
        if s ~= nil then 
          human_Name = string.match(_, "|(.+)$")
          print("TEST") -- this one is printed out as expected.
          print(_) -- this one is printed out as expected.
          print(human_Name) -- this one is empty. Nothing is printed.
        end
    end -- if 1
  end -- for