2010 Prius cold start?

Seems normal? Rattle from a head gasket failure actually makes the engine shake violently. I am not seeing that here. Check oil level? Starts on very cold mornings are always noisy.

 

That is normal, for a Prius.
If it was knocking, you wouldn't have to get out of the car to hear it.
Be smart and shut it off the second you hear it. Because it moisture in the cylinder.
Bad things will happen if you let it knock.

It might seem louder because of the colder air, and the engine is likely working a little harder
to warm up.

 

Advice vs advise.

Your video sounds really loud but it is hard to judge from your video.

Does it clear up and get quieter a minute or two later? If so capture the transition on video.

Does the engine shake and then get better? Capture that.

Early hg gasket problems present with a severe metal to metal rattle and the engine visibly shakes due to a hard misfire - both clearing up in less than a minute as the plugs burn off coolant which has leaked in when cool.

Typically no codes are set as it clears fast. Combustion gas in the coolant testing often provides a false negative and are unreliable on a Prius. If the coolant drops there is an advanced problem. If it does rattle severely twice or more in a month, it would be worth a quality dual view or an articulating borescope inspection.

If it has a hg leaking there is no real fix other than a new hg. Sometimes it can escalate to a replacement engine.