By the way
The very first palindromic date in ISO YYYYMMDD format after 1000-01-01 (Jan 01 1000) was 1001-10-01 (Oct 01 1001).
2020-02-02 is the 47th palindromic date in the YYYYMMDD format after the reference date 1000-01-01. In total, 372579 days have passed since then. The 331st and very last such date before the year 10000 is 9290-09-29 (Sep 29 9290). This will be the 3028132nd day after 1000-01-01 and therefore is still 2655553 days away (after 2020-02-02).
It is a little bit different in the DDMMYYYY format. The following applies here: 02.02.2020 is the 67th palindromic date after the reference date 01.01.1000. The last possible symmetrical date before the year numbers become five digits long one is 29.09.9092 which is the 335th such date in the list. Its just the 2955814th day after 01.01.1000.
Hint: Because of the Gregorian Calendar Reform of 1582, the numbers of days after 1001-01-01 are fictitious, strictly spoken. They are valid only then, if we adopt the reform for dates before 1582, subsequently. To get the real number of days after Jan 1 1000 for years after 1582 subtract 5 from each term representing a date after 1582. This applies to all palindromic dates after the 43rd in YYYYMMDD format, and after the 61st in DDMMYYYY format. The value 5 comes from the 10 skipped Gregorian dates between 1582-10-04 (Oct 4 1582) and 1582-10-15 (Oct 15 1582) minus the 5 additional Julian leap days in the years 1000, 1100, 1300, 1400 and 1500 which are not Gregorian leap years.