I think I remember receiving a few months ago some sort of communication about AdSense to one of my email addresses that wasn't my registered AdSense email address and that I wasn't aware AdSense knew existed. But other Google services did know the address. The email was probably legitimately from Google, but if it invited me to take any action, I probably didn't do it.
I think you're right to be suspicious of anything you receive at an email address that isn't the one you think the sender should have used.
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So as not to be misunderstood about links in emails, what I'm really suggesting is to IGNORE links in emails about your important online accounts. Don't click them. Don't copy and paste them.
The AdSense login URL is [
google.com...]
Use it to make a browser bookmark.
Always use that URL to visit your AdSense account.
Never visit it any other way.
Not by clicking. Not by copying and pasting.
If an email says something important is in your AdSense account, just log in using your bookmark. If it's so important, it will be easy to find.
The same for all other accounts: PayPal, online banks, etc.