Antag Selection Logging (#5847)

## Short description
Adds more robust logging to antag selection. (Aka, late joins, and round
number)

As I always say when I use AI, I used AI to help me, because I had no
clue what coderabbit was talking about on that second comment but I
figured "yeah I probably shouldn't flood the database".

## Why we need to add this
So we can group Grafana entries by round and track latejoin selections
<img width="1143" height="258" alt="image"
src="https://github.com/user-attachments/assets/246ac900-5a5f-406e-8428-add38b7e458d"
/>


## Checks
- [X] I do not require assistance to complete the PR.
- [X] Before posting/requesting review of a PR, I have verified that the
changes work.
- [X] I have added screenshots/videos of the changes, or this PR does
not change in-game mechanics.
- [X] I affirm that my changes are licensed under the [MIT
License](https://github.com/ss14Starlight/space-station-14/blob/Starlight/LICENSE.TXT)
and grant permission for use in this repository under its conditions.

Nothing player facing here

Author: wonderfulnewworld

Content.Server/Antag/AntagSelectionSystem.API.Assignment.cs

@@ -338,6 +338,18 @@ public bool TryAssignNextAvailableAntag(Entity<AntagSelectionComponent> gameRule
         ICommonSession session,
         int players)
     {
+        #region Starlight
+        return TryAssignNextAvailableAntag(gameRule, session, players, out _);
+    }
+
+    /// <summary>
+    /// Tries to find an open antag slot for a given player and returns the definition that was assigned.
+    /// </summary>
+    private bool TryAssignNextAvailableAntag(Entity<AntagSelectionComponent> gameRule, ICommonSession session, int players, [NotNullWhen(true)] out AntagSpecifierPrototype? assignedAntag)
+    {
+        assignedAntag = null;
+        #endregion
+
         foreach (var selector in gameRule.Comp.Antags)
         {
             if (!Proto.Resolve(selector.Proto, out var antag))
@@ -348,8 +360,13 @@ public bool TryAssignNextAvailableAntag(Entity<AntagSelectionComponent> gameRule
                 continue;
 
             // Try and assign this antag, if we fail, then try the next definition!
-            if (TryMakeAntag(gameRule, antag, session))
-                return true;
+            #region Starlight
+            if (!TryMakeAntag(gameRule, antag, session))
+                continue;
+
+            assignedAntag = antag;
+            return true;
+            #endregion
         }
 
         return false;
@@ -385,8 +402,13 @@ public bool TryMakeLateJoinAntag(ICommonSession session)
 
         foreach (var (uid, antag) in rules)
         {
-            if (TryAssignNextAvailableAntag((uid, antag), session, players))
-                return true;
+            #region Starlight
+            if (!TryAssignNextAvailableAntag((uid, antag), session, players, out var assignedAntag))
+                continue;
+
+            RecordLateJoinAntagAssignment((uid, antag), assignedAntag); // logging
+            return true;
+            #endregion
         }
 
         return false;