Docs examples 10/14: Rework messaging component examples

Part 10 of 14 in the stack that splits up the approved draft !6295 (closed) into reviewable pieces. The content is exactly what was reviewed there; I've only sliced it.

Related to #3575.

Pages: popover, tooltip, alert, toast, banner, broadcast message. Realistic content and contextual placement. Banner's introduction example now uses actual setup copy instead of an upgrade pitch, matching the page's own variant definitions, and broadcast message gains a Types section (banner vs notification) between Appearance and Behavior.

Safe to publish without the MRs after it.