Show merged rooms inside the host's card

Two cards side by side said nothing about whether the rooms were playing
together; now a room that joins the AVR moves into its card, under the
input it is playing, and leaving puts the card back in its own slot. The
button changes with it: Join Home Cinema when it stands alone, Leave when
it is in the group, since the card's position already says which it is.

Also fixes Separate everything, which sent a GET to a POST-only route and
so failed with a 405 and snapped the rooms straight back.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

README.md

@@ -10,7 +10,8 @@ Everything it does fits on one screen:
   on the next multiple of `VOLUME_STEP` — from 23 it goes to 25, not 28 —
   so the levels stay round. Hold to keep moving.
 - **Group** either room with the AVR — the AVR is always the host, so its
-  sound takes over whatever joins it
+  sound takes over whatever joins it. A room that joins moves *into* the
+  Home Cinema card, so one glance says what is playing together
 - **Ungroup** either room again, or all of them at once
 - **Change the AVR's input**, listed under the names you gave them, minus
   the sources you deleted in the AVR's setup menu