Unable to reproduce the issue on mac 10.13.3 using chrome reported version #69.0.3497.92 and latest canary #71.0.3551.3.
Attached a screen cast for reference.

Following are the steps followed to reproduce the issue.
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1. opened a profile window.
2. copied the profile's password into the system clipboard.
3. hit Command-V to paste the password into the profile window's password input.
4. observed that password got pasted into the profile window's password input using the Command-V keyboard shortcut.

fjarlq@ - Could you please check the issue on latest canary #71.0.3551.3 by creating a new profile without any apps and extensions and please let us know if the issue still persist or not. Also please check the attached screen cast and please let us know if anything missed from our end.

Thanks...!!

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Hi krajshree,

That isn't the profile window I'm referring to. Sorry, I should have included a screenshot in my original report. I'm talking about the profile switching window. Please let me know if my screenshot is unclear. Thanks.

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Thank you for providing more feedback. Adding the requester to the cc list.

For more details visit https://www.chromium.org/issue-tracking/autotriage - Your friendly Sheriffbot

fjarlq@ - Thanks for your clarification at comment #3. 
But on clicking the manage people button of avatar menu, no password field is prompted at manage people window, rather a new chrome window appears on clinking the icon.
Attached a screen cast for reference.

The password field at the manage people window appeared prior to M-69 on adding the supervised user, but the supervised user concept got removed at the follow link: 
https://www.google.com/url?q=https://bugs.chromium.org/p/chromium/issues/detail?id%3D829304%26can%3D1%26q%3Dcomponent%253AServices%253ESupervisedUser%2520%26colspec%3DID%2520Pri%2520M%2520Stars%2520ReleaseBlock%2520Component%2520Status%2520Owner%2520Summary%2520OS%2520Modified&sa=D&source=hangouts&ust=1537337671345000&usg=AFQjCNERopR_xlVehgg8gu0l5O6i2B1VOw.

Could you please let us know how the password field appeared in the screen shot at comment #3. Also a supervised user is seen. Is there any flag need to be enabled to get the desired manage people window as in the attached screen shot?

Thanks...!!

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I created the supervised user account a few years ago in order to enable password-protected Chrome profiles. This feature is still working fine for me, except for this bug involving the paste keyboard shortcut.

I was following this kind of advice: https://whatsabyte.com/internet/lock-google-chrome-profile/

Is there some newer functionality I should be using today to password-protect my Chrome profiles?

Thank you for providing more feedback. Adding the requester to the cc list.

For more details visit https://www.chromium.org/issue-tracking/autotriage - Your friendly Sheriffbot

The issue is related to using supervised user account in order to enable password-protected Chrome profiles. The supervised user account feature seems to have been deprecated as per the following link:
https://bugs.chromium.org/p/chromium/issues/detail?id=829304&can=1&q=component%3AServices%3ESupervisedUser%20&colspec=ID%20Pri%20M%20Stars%20ReleaseBlock%20Component%20Status%20Owner%20Summary%20OS%20Modified and in order to test the issue supervised user account need to be enabled.
Hence, removing the Needs-Bisect label and ccing jochen@ from https://bugs.chromium.org/p/chromium/issues/detail?id=865157 for further inputs as per C#6.

Thanks...!!

if you open the supervised user, I assume you get an info bar that tells you about the product's deprecation, correct?

I've never directly used the supervised user. The only reason I created it was to enable password protection on my other Chrome profiles, which I actually do use.

interesting use-case. Anyways, if you'd open the supervised profile, you'd get an infobar that tells you that the feature will cease to exist in M70, and the supervised profiles will no longer available (and consequently the password prompt also goes away).

Given that in M70 the feature doesn't exist anymore (and trunk is already on M71, we won't fix this).