feat: add collaborative math board and draw guess mode

backend/toolbox/models.py

@@ -0,0 +1,53 @@
+import uuid
+
+from django.conf import settings
+from django.db import models
+
+
+class BoardSession(models.Model):
+    class Mode(models.TextChoices):
+        COLLABORATE = "collaborate", "协作展示"
+        DRAW_GUESS = "draw_guess", "数学你画我猜"
+
+    class Status(models.TextChoices):
+        WAITING = "waiting", "等待加入"
+        ACTIVE = "active", "进行中"
+        COMPLETED = "completed", "已完成"
+        CANCELLED = "cancelled", "已取消"
+
+    id = models.UUIDField(primary_key=True, default=uuid.uuid4, editable=False)
+    code = models.CharField(max_length=6, unique=True)
+    mode = models.CharField(
+        max_length=16,
+        choices=Mode.choices,
+        default=Mode.COLLABORATE,
+    )
+    host = models.ForeignKey(
+        settings.AUTH_USER_MODEL,
+        on_delete=models.CASCADE,
+        related_name="hosted_board_sessions",
+    )
+    guest = models.ForeignKey(
+        settings.AUTH_USER_MODEL,
+        null=True,
+        blank=True,
+        on_delete=models.CASCADE,
+        related_name="joined_board_sessions",
+    )
+    target = models.CharField(max_length=40, blank=True)
+    host_score = models.PositiveSmallIntegerField(default=0)
+    guest_score = models.PositiveSmallIntegerField(default=0)
+    status = models.CharField(
+        max_length=16,
+        choices=Status.choices,
+        default=Status.WAITING,
+    )
+    expires_at = models.DateTimeField()
+    created_at = models.DateTimeField(auto_now_add=True)
+    completed_at = models.DateTimeField(null=True, blank=True)
+
+    class Meta:
+        ordering = ["-created_at"]
+
+    def __str__(self):
+        return f"{self.code} · {self.get_mode_display()}"