Track presence state per-device and combine to a user state. (#16066)

Tracks presence on an individual per-device basis and combine
the per-device state into a per-user state. This should help in
situations where a user has multiple devices with conflicting status
(e.g. one is syncing with unavailable and one is syncing with online).

The tie-breaking is done by priority:

    BUSY > ONLINE > UNAVAILABLE > OFFLINE

changelog.d/16066.bugfix

@@ -0,0 +1 @@
+Fix a long-standing bug where multi-device accounts could cause high load due to presence.

changelog.d/16170.bugfix

@@ -0,0 +1 @@
+Fix a long-standing bug where multi-device accounts could cause high load due to presence.

changelog.d/16171.bugfix

@@ -0,0 +1 @@
+Fix a long-standing bug where multi-device accounts could cause high load due to presence.

changelog.d/16172.bugfix

@@ -0,0 +1 @@
+Fix a long-standing bug where multi-device accounts could cause high load due to presence.

synapse/api/presence.py

@@ -20,18 +20,53 @@
 from synapse.types import JsonDict
 
 
+@attr.s(slots=True, auto_attribs=True)
+class UserDevicePresenceState:
+    """
+    Represents the current presence state of a user's device.
+
+    user_id: The user ID.
+    device_id: The user's device ID.
+    state: The presence state, see PresenceState.
+    last_active_ts: Time in msec that the device last interacted with server.
+    last_sync_ts: Time in msec that the device last *completed* a sync
+        (or event stream).
+    """
+
+    user_id: str
+    device_id: Optional[str]
+    state: str
+    last_active_ts: int
+    last_sync_ts: int
+
+    @classmethod
+    def default(
+        cls, user_id: str, device_id: Optional[str]
+    ) -> "UserDevicePresenceState":
+        """Returns a default presence state."""
+        return cls(
+            user_id=user_id,
+            device_id=device_id,
+            state=PresenceState.OFFLINE,
+            last_active_ts=0,
+            last_sync_ts=0,
+        )
+
+
 @attr.s(slots=True, frozen=True, auto_attribs=True)
 class UserPresenceState:
     """Represents the current presence state of the user.
 
-    user_id
-    last_active: Time in msec that the user last interacted with server.
-    last_federation_update: Time in msec since either a) we sent a presence
+    user_id: The user ID.
+    state: The presence state, see PresenceState.
+    last_active_ts: Time in msec that the user last interacted with server.
+    last_federation_update_ts: Time in msec since either a) we sent a presence
         update to other servers or b) we received a presence update, depending
         on if is a local user or not.
-    last_user_sync: Time in msec that the user last *completed* a sync
+    last_user_sync_ts: Time in msec that the user last *completed* a sync
         (or event stream).
     status_msg: User set status message.
+    currently_active: True if the user is currently syncing.
     """
 
     user_id: str