Host specific passwords for interactive use is difficult for humans, and so is bad policy.
Start with an auth factor better than passwords. Your ssh keys are an obvious example for Linux or POSIX systems, there are others. Personal keys or certificates just for you, so your access can be traced. Use these on every host, such as with a central user directory.
For automated non-human users this single strong auth factor should be enough. Passwords and other people focused secondary auth factors are annoying to automate. They need to be provided plain-text without interaction, which defeats the purpose. Focus instead on improving the processes around automation, ensuring that only the approved scripts run, and not by a person.
For interactive use by a human, passwords still are not great, but may be an easy to implement other auth factor anyway. And so for a person, sudo rules for privileged access might use PASSWD. Use your centrally managed password, again possibly in a user directory.
Yes, you could have host specific passwords for your access, look them up in a secure password manager, and paste them in. But why. You could instead skip the password manager and type a long easy to remember passphrase you use everywhere. As XKCD 936 promised, I cannot forget "Correct horse battery staple" even if I tried.
In theory a password only used on a subset of hosts is less exposure when compromised, but losing any privileged credential is not good. How do you know an attacker has not used that to gain persistent access to your systems?
Separate accounts and passwords could be justified for security critical systems. For example, secret management systems, user directories, backup archival systems. A compromised credential in these could result in data exfiltration and exposure to ransom. So avoid using your regular account for privileged access.