feat: add start_time(s) for AutoShardedClient (#1482)

* feat: add start_time(s) for AutoShardedClient

* feat: make start_times a dict

* docs: make start_times docstring clearer

Co-authored-by: Sophia <41456914+i0bs@users.noreply.github.com>
Signed-off-by: Astrea <25420078+AstreaTSS@users.noreply.github.com>

---------

Signed-off-by: Astrea <25420078+AstreaTSS@users.noreply.github.com>
Co-authored-by: Sophia <41456914+i0bs@users.noreply.github.com>

Author: AstreaTSS

interactions/client/auto_shard_client.py

@@ -1,5 +1,6 @@
 import asyncio
 import time
+from datetime import datetime
 from collections import defaultdict
 from typing import TYPE_CHECKING, Optional
 
@@ -68,6 +69,16 @@ def latencies(self) -> dict[int, float]:
         """
         return {state.shard_id: state.latency for state in self._connection_states}
 
+    @property
+    def start_time(self) -> datetime:
+        """The start time of the first shard of the bot."""
+        return next((state.start_time for state in self._connection_states), MISSING)  # type: ignore
+
+    @property
+    def start_times(self) -> dict[int, datetime]:
+        """The start times of all shards of the bot, keyed by each shard ID."""
+        return {state.shard_id: state.start_time for state in self._connection_states}  # type: ignore
+
     async def stop(self) -> None:
         """Shutdown the bot."""
         self.logger.debug("Stopping the bot.")