web: expose thinking_token_budget in text-generation launcher

[cswaney]

Surfaced during the vLLM v0.26 audit (#515).

Context

vLLM v0.22 added `thinking_token_budget` — a per-request cap on how many tokens the model spends "thinking" before producing the visible answer. It complements the existing Disable Thinking toggle: instead of the binary on/off choice, users could allow reasoning but bound its cost.

The Disable Thinking toggle maps to a launch-time flag (`--default-chat-template-kwargs`). `thinking_token_budget` is per-request, so it belongs on the completions/chat body, not the launcher — likely in the parameters sidebar (`SidebarContainer`'s Parameters section for text-generation), alongside `temperature` and `max_tokens`.

Scope

• Add a numeric input to the text-generation parameters form. Default: empty (no budget, vanilla thinking behavior).
• Include `thinking_token_budget: ` in the completion request body when set. Applies to both streaming and non-streaming paths.
• Add a small explainer in help text: it only takes effect for models that support thinking mode; on non-thinking models it is ignored.
• Tests for the request body shape.

Notes

• Complements Disable Thinking rather than replacing it. Disable Thinking is a launch-time choice (affects the chat template); `thinking_token_budget` is a per-request choice.
• Not a bug — pure feature request.