Send reasoning content back to the model across turns via the reasoning_content API field (#21036)

* webui: send reasoning_content back to model in context

Preserve assistant reasoning across turns by extracting it from
internal tags and sending it as a separate reasoning_content field
in the API payload. The server and Jinja templates handle native
formatting (e.g. <think> tags for Qwen, GLM, DeepSeek...).

Adds "Exclude reasoning from context" toggle in Settings > Developer
(off by default, so reasoning is preserved). Includes unit tests.

* webui: add syncable parameter for excludeReasoningFromContext

* chore: update webui build output