Looking For Help Diagnosing Noise & Wobble

I will try to keep it as short as possible, but I figure it's important to have as much information as possible.

I recently replaced my chain and cleaned the cassette and back wheel (gently with appropriate products) while I had it off. After putting everything back on with the new chain I am left with a chatter around the back hub when pedaling and a very noticeable wobble of the whole hub when spinning (it's quite a bit more prevalent than it appears in the video). I don't know if they're related, or two separate issues. I have tried my best to figure out what is going on, but am stumped.

– There is no wobble/play in the rear hub when trying to move it around by hand.

– The cassette and chainring are quite new and don't show any visible signs of wear

– On that note the previous chain was not very warn at all.

– The old a new chains are an identical length.

– I have checked to make sure the locknuts on the cones aren't loose.

– I have made sure everything on the rear derailleur is dialed in.

Any help is appreciated.