Is my right to be in Slovakia limited to the specific activity I applied for?

Temporary residence for a specific activity is purpose-bound. The permission you receive is for the lecturing, scholarship participation, internship or other declared activity, not a general right to work or do anything else in Slovakia.

If the activity changes or ends, your basis for residence is affected, and continuing a different activity may require a different permit. Keep the documents proving your activity current, and if your situation changes, get advice on whether you need to switch to another residence category rather than relying on the existing one.