[Notif redesign] Fix remote input history not appearing

There was an issue where remote input history would not appear at all
except for notifications with the default style. This was because I'd
accidentally updated the id in the xmls instead of the layout :/

I also renamed the layout now to better reflect what it actually is,
improving disambiguation between this and the
notification_template_smart_reply_container.

Bug: 378660052
Test: visual test, screenshot tests to come later
Flag: android.app.notifications_redesign_templates
Change-Id: Icc62198cc02bda3010ea99b3db25713de8ba5a95