Experimental mod ruling given the creator is absent:
This question counts all launches of Starships and Starship prototypes (excluding Starhopper), including tests, and regardless of success. "Launch" means liftoff from the pad, however slight, under the thrust of rocket engines (Starship's own, or a booster's).
A launch must take place before 2040, local time at the launch site, in order to qualify.
A list of Starship flight tests so far can be found here:
https://en.wikipedia.org/wiki/SpaceX_Starship_flight_tests
Current qualifying launches include:
150m hop of SN5 on Aug 1st 2020
150m hop of SN6 on Sep 3rd 2020
12.5km hop of SN8 on Dec 9th 2020
10km hop of SN9 on Feb 2nd 2021
10km hop of SN10 on Mar 3rd 2021
10km hop of SN11 on Mar 30th 2021
10km hop of SN15 on May 5th 2021
Integrated flight test 1, Apr 20th 2023
Integrated flight test 2, Nov 18th 2023
For a total of 9 at time of writing.