[Tau2] Support separate LLM credentials and base URLs for client and agents (tau2, proxy-agent)

[aviweit]

Background

Currently, both the client and agents (tau2, proxy-agent) rely on LiteLLM for model access. LiteLLM reads configuration from global environment variables (e.g., OPENAI_API_KEY, OPENAI_BASE_URL), which makes it difficult to differentiate credentials and endpoints between components.
In practice, we need the ability to configure different LLM providers, API keys, and base URLs independently for:

• Client
• tau2 agent
• proxy-agent

This is especially important in scenarios such as:

Using different providers per component (e.g., OpenAI for client, Azure/OpenAI-compatible proxy for agents)
Routing agent traffic through internal gateways / proxies
Applying different rate limits, auditing, or billing scopes
Supporting multi-tenant or environment-specific configurations

Problem

Both tau2 and proxy-agent currently inherit the same global OPENAI_* environment variables via LiteLLM, which:

• Prevents isolating credentials between components
• Forces all components to use the same base URL and API key
• Creates conflicts when different configurations are required simultaneously

Proposed Solution

Introduce explicit, per-component LLM configuration support.
Option 1: Namespaced Environment Variables
Allow defining separate environment variables for each component, for example:

# Client
SB_CLIENT_OPENAI_API_KEY=
SB_CLIENT_OPENAI_BASE_URL=

# Tau2
SB_TAU2_OPENAI_API_KEY=
SB_TAU2_OPENAI_BASE_URL=

# Proxy Agent
SB_SPA_AGENT_OPENAI_API_KEY=
SB_SPA_OPENAI_BASE_URL=

Each component should initialize LiteLLM with its own configuration instead of relying on global OPENAI_* variables.