Pushes the resolved UI locale to the connected sidecar node.

Mirrors Planck.Headless.Widgets's dispatch shape, but one-way and with no meaningful fallback value to return — this is a best-effort push, not a read a caller is waiting on. Planck.Web.Locale.Plug calls set/1 on every request (it has no cheap way to know in advance whether the locale actually changed), which is exactly why the remote side (Planck.Agent.Sidecar.set_locale/1) is written to be a no-op when it hasn't.