Can someone explain why it is considered as such, also with regard to forensics (if that makes any difference)? The original definition of privacy looks somewhat archaic in this case.

E.g.: someone follows you everywhere with a camera - it's privacy invasion. Some public camera films you accidentally at a specific place - it is not, though it's clearly you in the video. Seems like intent and focus are key here, and your image is not invasive by itself, but only if someone focuses on you. We leave DNA everywhere just like we leave images on every camera, but (to me) it's only privacy invasion if someone builds many fragments together or pauses to "look" into your business there. DNA itself is as private as your look - everyone can see it unless you actively counter it by physical means.

But the police didn't focus on her, they focused on evidence, just as if some camera filmed her in that house and they'd look at that footage, not at some drone footage tracing specifically her to see if her route maybe includes that house.

Storing DNA from previous encounters is ~ like storing your id photo (i.e. absolutely neutral info, lacking any context). Does this part invade privacy, maybe? But what's private here?