One unfortunate-ish thing of storing it in TextControlState is that we
can't preserve it across type changes, but that seems ok for now
according to my conversations with Serg.
In the future we might want to move the value to HTMLInputElement itself
or something, we'll see, but this should help folks fix some
long-standing quality issues in the password manager / autofill
implementation.
Differential Revision: https://phabricator.services.mozilla.com/D150148