What would be a more formal way to say something like
The data has all been processed by now, so there's no need for further action
in an email?
I'm worried that "by now" might sound a little aggressive.
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There is nothing informal about "by now" (nor are emails noted for a high degree of formality).
Your point about your example sounding somewhat aggressive has nothing to do with formality, but about perception and good manners. I can see that in certain contexts many would feel the example to be dismissive or denigrating, but I doubt that merely replacing "by now" would alter the perceived tone.
Thank you for your offer, but the data have already been processed.