Add resizable room panel, searchable user picker, and direct room membership

Room info panel is now user-resizable (fixing a layout clip at narrow
widths), and every user-selection spot (room membership, admin ownership
transfer) uses a new searchable UserPicker instead of raw text input or
prompt(). Member rows fold role + actions into a single inline dropdown
instead of a row of buttons, so the member list stays usable as rooms grow.

Room invites (the accept/decline flow) are replaced by adding a user to a
room directly -- an admin/owner picks someone and they're a member
immediately, with a "you've been added" notification email instead of an
invite email. Drops the now-unused room_invites table.

frontend/src/api/rooms.ts

@@ -46,6 +46,13 @@ export function listRoomMembers(roomId: string): Promise<RoomMember[]> {
   return apiFetch<RoomMember[]>(`/api/rooms/${roomId}/members`)
 }
 
+export function addRoomMember(roomId: string, userId: string): Promise<RoomMember> {
+  return apiFetch<RoomMember>(`/api/rooms/${roomId}/members`, {
+    method: 'POST',
+    body: JSON.stringify({ user_id: userId }),
+  })
+}
+
 export function removeMember(roomId: string, userId: string): Promise<void> {
   return apiFetch<void>(`/api/rooms/${roomId}/members/${userId}`, { method: 'DELETE' })
 }