Password entry: are "paste from password manager" and "eyeball to view passwords" mutually-exclusive features?
Password managers are not meant to hide your passwords from yourself
It's as simple as that. To whit: most password managers let you view your own password anytime you want anyway. I say "most" only because I haven't used them all. I've worked with a few sites where auto fill doesn't work for reasons outside the password managers control. Therefore viewing/copying your own passwords is a necessity. IMO a password manager that doesn't let you view your own secrets is a broken password manager.
If you can use the password manager to view your own password, then an individual site that refuses to display a password at the user's request in an attempt to hide their password from themselves has grossly missed the bigger picture.
Some people use password managers, some don't
The ability to paste is very helpful when using password managers. The ability to view as you type is helpful for people who are typing their passwords (especially on phones). These are two different features for two different groups of people, both of whom can be expected to use a given site. Therefore to say you only need one of these features at a time is just silly...
[self-answer]
You can trivially unmask a password field with right-click > Inspect Element > change type="password" to type="". So there's really no reason not to put a "View your password" eyeball on a web UI.
Testing on GitHub's front page, which does not have the eyeball button:
There are many good answers already, but I would like to add one point.
Quite frequently, I have to enter passwords on computers that I don't have my password manager installed on. When that happends, I read the password on my cell phone and enter it on the computer. This would also frequently be the case for those who uses a local password manager on just one device.
When entering random gibberish, it is very easy to get lost. Erasing everything and starting over is pain in the butt. If I didn't have the ability to view the password while typing it so I can easily correct mistakes, I would be lazy and pick much shorter passwords.
TL;RD: Allowing to view passwords while typing makes me pick better passwords, even if I am using a password manager.