Re: I know not of these matters...
I think most of your statements are wrong there. We'll start with the first one. You can violate privacy without immediately sending the contents of the clipboard off. As a basic example, if you copied it into an internal buffer and used it to perform on-device metrics, even if you never sent those metrics, it could be violating the privacy of data stored in the clipboard. Sure, it's relatively low-level and users should be careful (that is assuming this app only did this while in the foreground), but don't assume that violating privacy requires phoning home. In this case, I don't think LinkedIn was using this as a sneaky data collection feature because it would be so fragile. I think it's more likely that some coder thought it would be useful and didn't think of alternatives or the downsides.
Now on to the code part. You say that checking the clipboard content "is absolutely required if you want to implement "Paste" into anything other than text views and text fields." Not true, because you still only have to read from the clipboard when a user presses that button. The issue here is checking the content in a loop without any button. Then, you said that "you want to know what's in there so you don't have for example a "Paste" button if there is stuff that you can't paste." I disagree, because I find hiding controls that you sometimes have and sometimes don't confuses the users, but that's a subjective UX thing. You can implement format-specific paste in a number of ways, including cancelling a paste operation without changing the original content if the contents are not compatible. You can warn the user or not as you desire.
"And then there's the fact that in Windows, Linux, MacOS, Android, and iOS up to 13.0, everyone does it. For good reasons."
You are assuming the reasons are good. Frequently, I find that good programs wait for me to paste in the contents of my clipboard rather than snatching potentially incorrect data out, though I will admit I've seen some go the other way.
Unless you really need real-time monitoring of clipboard contents for some reason, you are also making your application do a lot of pointless busy looping. This isn't great for performance or power usage if you do it for long enough.