that noise combined with the coolant loss sounds like a bad water pump to me. But I can't say there is a reason for that besides your description and video. I'm still not 100% sure i understand what you have had fixed in the steering (did they replace the rack or just the inner tie rod? seems like rack) and that noise could also be the power steering pump not having enough fluid from improper filling during install And now that the steering burped it is low.