fix(proxy): use >= in _team_max_budget_check to match other budget checks

Fixes #28020

_team_max_budget_check used `>` while every other budget enforcement
path (key, organization, budget windows) uses `>=`. A team whose spend
hit exactly `max_budget` was still allowed through.

Change `>` to `>=` and add a regression test that asserts
BudgetExceededError is raised when spend == max_budget.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

litellm/proxy/auth/auth_checks.py

@@ -3694,7 +3694,7 @@ async def _team_max_budget_check(
             fallback_spend=team_object.spend or 0.0,
         )
 
-        if math.isfinite(team_object.max_budget) and spend > team_object.max_budget:
+        if math.isfinite(team_object.max_budget) and spend >= team_object.max_budget:
             if valid_token:
                 call_info = CallInfo(
                     token=valid_token.token,

tests/test_litellm/proxy/auth/test_auth_checks.py

@@ -2297,6 +2297,42 @@ async def test_team_budget_check_reads_from_spend_counter():
         assert exc_info.value.current_cost == 1.5
 
 
+@pytest.mark.asyncio
+async def test_team_budget_check_raises_when_spend_equals_max_budget():
+    """Team budget check should raise BudgetExceededError when spend == max_budget,
+    matching the behavior of key / org / budget-window checks which all use >=.
+
+    Regression test for the inconsistency where _team_max_budget_check used `>`
+    while every other budget enforcement path used `>=`.
+    """
+    from litellm.proxy.utils import ProxyLogging
+
+    team_object = LiteLLM_TeamTable(
+        team_id="test-team-equal",
+        spend=0.0,
+        max_budget=10.0,
+    )
+    valid_token = UserAPIKeyAuth(token="test-token", team_id="test-team-equal")
+
+    proxy_logging_obj = ProxyLogging(user_api_key_cache=None)
+    proxy_logging_obj.budget_alerts = AsyncMock()
+
+    async def mock_get_current_spend(counter_key, fallback_spend):
+        if counter_key == "spend:team:test-team-equal":
+            return 10.0  # exactly at the cap
+        return fallback_spend
+
+    with patch("litellm.proxy.proxy_server.get_current_spend", mock_get_current_spend):
+        with pytest.raises(litellm.BudgetExceededError) as exc_info:
+            await _team_max_budget_check(
+                team_object=team_object,
+                valid_token=valid_token,
+                proxy_logging_obj=proxy_logging_obj,
+            )
+        assert exc_info.value.current_cost == 10.0
+        assert exc_info.value.max_budget == 10.0
+
+
 @pytest.mark.asyncio
 async def test_end_user_budget_check_reads_from_spend_counter():
     """End-user budget check should use get_current_spend when counter exists."""