Replaced the power steering pump as well as put an INA tensioner on. Still some tensioner movement. Hopefully it's no big deal.

Update

I replaced the bad alternator pulley. Upon test run, tensioner still had noticeable oscillation. It seemed slightly better and less noisy, but still moving.

The pulley I'm replacing first is the Alternator clutch pulley - from what I can tell that is a splined setup?

Also if I order the power steering pump pulley - any recommended pullers?

EDIT: from what I've read I may be better off just getting a new whole PS pump if I go that route..

I've ordered a new alternator pulley. Verified part number for my vehicle/alternator.
Crossing my fingers it will fix it. Will report back after replacement.

185k miles.

I put a screwdriver in the alternator to hold the shaft and attempted to turn it both ways and it didn't turn either.

Took belt back off:

Should the alternator pulley spin freely in both directions? Any tests I can run on the pulleys to check their functionality?

Uh oh. Thanks for checking.

I had someone step on the gas a little to bring RPMs up from idle and the movement persisted. So it doesn't appear to be from the idle.

Video link:

Also - no squealing from the belt.

I will post a video later of what's going on. Thank you all for your concern.

I will take a look today and observe all the pulleys to check for issues.

Alternator is roughly 1.5 years old.