Today I got email from Apple: Your Apple ID was used to sign into iCloud.

I too get this. But it says I used Chrome as web browser, even though I used Microsoft Edge. Why does

it claim that I used Chrome browser?

if it isn't addressed to you by name it's phishing. Do not follow any links in it. If you want to check your ID page or contact Apple go directly to the correct URLs.

Also, the e-mail isn't an Apple e-mail address.

It's a fake - do not follow the link: it's an attempt to get your credit card details and/or sign-in. Real emails from Apple will always address you by name.

I get it, more security, but is it really needed everytime Google Chrome updates on my same computer, I have to re-login because Apple thinks it's a new device???

Sorry, but what does your question have to do with emails?

GB