#33321 [Bug]: team, end-user, tag, and model budgets admit requests at the exact limit
### Check for existing issues
- [x] I have searched the existing issues and checked that my issue is not a duplicate
### What happened?
Hard-budget checks use different boundary operators for the same product concept on current `litellm_internal_staging` at commit `65ca095d4d15a82372e53a547a2390a69f7e1797`
Key, user, organization, and centralized team-member checks reject when current spend is equal to the configured maximum by using `>=`
The following active checks admit at equality:
| Scope | Current condition | Result when spend == max | | --- | --- | --- | | Team | `spend > team_object.max_budget` | admitted | | End user | `end_user_spend > end_user_budget` | admitted | | Tag | continue while `tag_spend <= max_budget` | admitted | | Virtual-key model | `_current_spend > max_budget` | admitted | | End-user model | `_current_spend > max_budget` | admitted |
Relevant code:
- [team check](https://github.com/BerriAI/litellm/blob/65ca095d4d15a82372e53a547a2390a69f7e1797/litellm/proxy/auth/auth_checks.py#L3881-L3928) - [end-user check](https://github.com/BerriAI/litellm/blob/65ca095d4d15a82372e53a547a2390a69f7e1797/litellm/proxy/auth/auth_checks.py#L1080-L1096) - [tag check](h…