MYSQL Inventory count per date range
It is quite simole your inner SELECT counts every row that it gets, from timetable so you have to rstrict also the inner SEELCT


CREATE TABLE timetable (
id INT(6) UNSIGNED AUTO_INCREMENT PRIMARY KEY,
project_id INT(6) NOT NULL,
item VARCHAR(35) NOT NULL,
quantity INT(3) ZEROFILL NOT NULL,
dt_start DATETIME,
dt_END DATETIME
);

INSERT INTO timetable (project_id,item,quantity,dt_start,dt_end)
VALUES
(1234, 'table', 50, '2021-01-10 10:00:00', '2021-01-12 10:00:00'),
(1234, 'chair', 200, '2021-01-10 10:00:00', '2021-01-12 10:00:00'),
(1234, 'light', 2, '2021-01-10 10:00:00', '2021-01-12 10:00:00'),
(5678, 'table', 25, '2021-01-12 10:00:00', '2021-01-15 10:00:00'),
(5678, 'light', 3, '2021-01-12 10:00:00', '2021-01-15 10:00:00'),
(9876, 'table', 10, '2021-01-10 10:00:00', '2021-01-14 10:00:00'),
(9876, 'chair', 100, '2021-01-10 10:00:00', '2021-01-14 10:00:00'),
(2323, 'light', 10, '2021-01-12 10:00:00', '2021-01-15 10:00:00');

CREATE TABLE calendar (dt date not null primary key);
INSERT INTO calendar (dt)
VALUES ('2021-01-9'),('2021-01-10'),('2021-01-11'),('2021-01-12'),
('2021-01-13'),('2021-01-14'),('2021-01-15'),('2021-01-16'),
('2021-01-17'),('2021-01-18'),('2021-01-19'),('2021-01-20');




SELECT 
  t1.*, 
  (SELECT CAST(SUM(t2.quantity) AS CHAR)
   FROM timetable t2 
   WHERE t2.item = t1.item
   AND    ('2021-01-13 10:00:00' &lt;= date(dt_END))
  AND
  (date(dt_start) &lt;= '2021-01-18 10:00:00')
) AS itm_sum
FROM timetable t1
    WHERE
  ('2021-01-13 10:00:00' &lt;= date(dt_END))
  AND
  (date(dt_start) &lt;= '2021-01-18 10:00:00')


id | project_id | item  | quantity | dt_start            | dt_END              | itm_sum
-: | ---------: | :---- | -------: | :------------------ | :------------------ | :------
 4 |       5678 | table |      025 | 2021-01-12 10:00:00 | 2021-01-15 10:00:00 | 35     
 5 |       5678 | light |      003 | 2021-01-12 10:00:00 | 2021-01-15 10:00:00 | 13     
 6 |       9876 | table |      010 | 2021-01-10 10:00:00 | 2021-01-14 10:00:00 | 35     
 7 |       9876 | chair |      100 | 2021-01-10 10:00:00 | 2021-01-14 10:00:00 | 100    
 8 |       2323 | light |      010 | 2021-01-12 10:00:00 | 2021-01-15 10:00:00 | 13     


db&lt;&gt;fiddle here