Yeah there's even an "Agent SDK" from Anthropic that manages Claude CLI sessions for you, and a separate token budget for apps that use it, on top of the subscription tokens.
even that was relaxed by Anthropic and they stopped chasing token prices for Agent SDK. I routinely use Agent SDK with my subscription and it doesn't come out of a separate budget. Their ToS vaguely says just don't use your personal subscription for commercial resale purposes.