I would unpivot the tickets table to compute the backlog on any given day, then bring the dates table with a join.

select d.date, c.cnt
from dates d
left join (
    select x.dt, sum(x.val) cnt
    from tickets t
    cross apply ( values (opened_date, 1), (closed_date, -1) ) x(dt, val)
    group by x.dt
) x on x.dt = d.date

The upside of this solution is that is scans the tickets table only once, as opposed to other options involving a correlated subquery with inequality conditions (or a lateral join), that needs to be re-executed for each and every date.

When asking questions like this it's really helpful to provide easily reproducible DDL/DML. This makes it easier for folks to answer your question.

Consider:

DECLARE @Dates TABLE (Date DATE, Year INT);
INSERT INTO @Dates (Date, Year) VALUES
('2021-02-19', 2021), ('2021-02-20', 2021), ('2021-02-21', 2021), 
('2021-02-22', 2021), ('2021-02-23', 2021), ('2021-02-24', 2021);
DECLARE @Tickets TABLE (TicketNumber VARCHAR(8), OpenedDate DATE, ClosedDate DATE);
INSERT INTO @Tickets (TicketNumber, OpenedDate, ClosedDate) VALUES
('00000001', '2021-02-01', '2021-02-23'), ('00000002', '2021-02-16', '2021-02-19'), ('00000003', '2021-02-21', NULL        ),
('00000004', '2021-10-01', '2021-01-23'), ('00000005', '2021-02-01', '2021-02-19'), ('00000006', '2021-02-05', '2021-02-19'),
('00000007', '2021-02-01', '2021-02-18'), ('00000008', '2021-02-23', '2021-02-24'), ('00000009', '2021-02-22', '2021-02-22'),
('00000010', '2021-02-01', '2021-02-21');

I've adjusted your example data here as I think you intended the ticket numbers to be different for each row.

To produce a result set which shows the number of open tickets all you really need is a LEFT OUTER JOIN from the dates table to the tickets table. Since we want the date to be within a range (which is essentially endless when there is no closed date) we can use a BETWEEN as the predicate, and then aggregate by the date. A LEFT OUTER JOIN is used so we get a 0 when there are no tickets for that day. Using INNER JOIN would result in the row being excluded from the result set.

SELECT d.Date, COUNT(t.TicketNumber) AS OpenTickets
  FROM @Dates d
    LEFT OUTER JOIN @Tickets t
      ON d.Date BETWEEN t.OpenedDate AND COALESCE(t.ClosedDate,'9999-12-31')
 GROUP BY d.Date