I completely understand that the scale and scope of abuse in tech can be much higher than with other services due to automation, but I don't see how its reasonable to question whether my stuff is still my stuff because I've entrusted it to a third party.
Yes.
> Is it really yours?
Yes, though obviously it depends on the service, and my agreement with them. Most of my photos, for example, are backed up in OneDrive, which works quite well for my purposes.
> What if your professional organization says "we've installed some big data analytics", or "whoops we lost all your data"?
Good question! My photos, for example, exist on my local computer, Microsoft OneDrive, and on Google Photos. The odds of losing them are, frankly, as non-existent as possible. Multiple storage locations, IMO, are a good way to mitigate the relatively low risk of losing cloud data. Also, almost no effort on my part is required.