## Environment - litellm `1.83.4` and `1.83.12` - Provider: `anthropic` - Python 3.13

## What breaks

`litellm.acount_tokens(model='anthropic/…', api_base='https://my-proxy/…', api_key='…')` sends its request to the default `https://api.anthropic.com/v1/messages/count_tokens` instead of the provided `api_base`. Callers routing through proxies (local aggregators, OAuth-fronted gateways, custom rotation services) get 401/403/network-unreachable, not a count.

## Root cause

`litellm.acount_tokens` (`litellm/main.py`) correctly packs `api_base` into `deployment["litellm_params"]["api_base"]` before calling the provider's `token_counter_instance.count_tokens(...)`.

`AnthropicTokenCounter.count_tokens` (`litellm/llms/anthropic/count_tokens/token_counter.py`) then reads `api_key` out of `litellm_params` but **does not read `api_base`**, and calls `handle_count_tokens_request` without passing it:

```python litellm_params = deployment.get("litellm_params", {}) api_key = litellm_params.get("api_key") # pulled # api_base = litellm_params.get("api_base") # MISSING

result = await anthropic_count_tokens_handler.handle_count_tokens_request( model=model_to_use, messages=mess…