I bought a new chain and cassette for my road bike. The bike is about 10 years old from estimation (9 speed shimano). I assumed I replaced all the parts correctly, but now whenever I stop pedaling, I feel some resistance as the free wheel is not working correctly. At slow speeds, the cassette keeps spinning when I stop pedalling, albeit with less force than the wheel. The casette is then blocked by the chain which causes the chain to skip, making a lot of noise. If I put my bike upside down and turn the pedal backwards, the rear wheel starts rotating backwards as well.
I've googled and the only suggestions I've found are about servicing the freehub part in the wheel. However, I never had a single problem with this, and the first moment I rode after replacing the chain and cassette, it started happening. Therefore it would be very coincidental if it is not related to the new casette. Any pointers?
EDIT: here are two videos I made, with the first showing that the wheel and casette are connected when the cassette is not turning or turning backwards, and the second showing the range in which I can turn the cassette.