#33325 [Bug]: model_max_budget reads pod-local spend and can exceed the cap across replicas
### Check for existing issues
- [x] I have searched the existing issues and checked that my issue is not a duplicate
### What happened?
The virtual-key and end-user `model_max_budget` admission check can use pod-local spend instead of shared Redis spend on current `litellm_internal_staging` at commit `65ca095d4d15a82372e53a547a2390a69f7e1797`
[`_PROXY_VirtualKeyModelMaxBudgetLimiter.__init__`](https://github.com/BerriAI/litellm/blob/65ca095d4d15a82372e53a547a2390a69f7e1797/litellm/proxy/hooks/model_max_budget_limiter.py#L21-L32) does not initialize its `RouterBudgetLimiting` parent, so the parent periodic synchronization task is not started for this hook
More importantly, [the admission lookup](https://github.com/BerriAI/litellm/blob/65ca095d4d15a82372e53a547a2390a69f7e1797/litellm/proxy/hooks/model_max_budget_limiter.py#L175-L201) calls `DualCache.async_get_cache`, which returns an in-memory hit before consulting Redis
Success logging increments local model spend and pushes increments to Redis, but a pod with an existing local value does not Redis-first refresh before deciding whether to admit the next request
That differs from the primary key, user, team, and tag hard-budg…