I've found lots of information about JavaScript injections, but didn't find any specific regarding password field.
For my test GMail account I was able to set the next password <Script>alert(document.cookie);</script> and it works correctly.

Should I just encode the < and > to their HTML equivalent?
How to handle such passwords?
Edit #1:
I store passwords in DB as hashes (and no issues for JavaScript injections here).
And I want to add a toggle for Password Visibility.
In this case I should encode the < and > to their HTML equivalent and that's it?
I used the next advice:
for a
Password toggle Visibility:2.1 if it is implemented with a plain
<input>, you don't have to do anything (no JavaScript injections here).2.2 if it is implemented with a
<span>,<div>, etc, then you have to HTML-encode it (and note that you also have to worry about&characters).