@Laurine ********
ahhh, you are on a "trailing spouse" extension (married to another foreigner who legally works here) AND you are correct you can't 'work' on that extension type.
The ONLY way you'd be able to change it in country would be to go in to your immigration office, cancel your current extension of stay (the one piggybacked to your spouse's employment extension), then immediately apply for a 60 day covid extension, and once you get that get documentation from the university/foundation/company that you're going to intern for and go apply for the in country 90 day ED visa at your immigration office.
You need to take a representative from your employer to make SURE this can be done before you cancel the extension you're on.