Running sum total over 14 days for each date
This is a bit tricky but very fast query that counts how many days customer spent idle up to the date. You can use it as subquery to refine by additional conditions. I hope it is selfexplanatory enough.
Unfortunately dbfiddle works pretty bad with UDVs so I can't provide a working sample.
SELECT cust_id
     , date
     , new_transactions
     , total_transactions
     , IF( @curr_cust_id &lt;=&gt; @curr_cust_id := cust_id,
       /*THEN*/ IF( new_transactions = 0,
                /*THEN*/ @idle4 := @idle4 + 1,
                /*ELSE*/ @idle4 := 0 
                /*FI*/ ), 
       /*ELSE*/ @idle4 := 0
       /*FI*/ ) AS idle_for
  FROM customer_tbl
 WHERE ( TRUE OR @idle4 := 0 )       -- UDV initialization
 ORDER BY cust_id ASC
        , date ASC
;

+---------+------------+------------------+--------------------+----------+
| cust_id |       date | new_transactions | total_transactions | idle_for |
+---------+------------+------------------+--------------------+----------+
|   10001 | 2020-02-01 |                1 |                  1 |        0 |
|   10001 | 2020-02-02 |                1 |                  2 |        0 |
|   10001 | 2020-02-03 |                0 |                  2 |        1 |
|   10001 | 2020-02-03 |                0 |                  2 |        2 |
|   10001 | 2020-02-04 |                0 |                  2 |        3 |
|   10001 | 2020-02-05 |                0 |                  2 |        4 |
|   10001 | 2020-02-06 |                1 |                  3 |        0 |