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.

backend/app/schemas/room.py

@@ -45,6 +45,10 @@ class RoomMemberRead(BaseModel):
     joined_at: datetime
 
 
+class RoomMemberAdd(BaseModel):
+    user_id: uuid.UUID
+
+
 class RoomMemberRoleUpdate(BaseModel):
     role: RoomRole