server: real-time reasoning interruption via control endpoint (#23971)

* server: real-time reasoning interruption via control endpoint

Builds on the manual reasoning budget trigger from #23949. Adds a
CONTROL task that mirrors the CANCEL path on the live slot and calls
common_sampler_reasoning_budget_force to end thinking mid-generation.
POST /v1/chat/completions/control with { id_slot, action }, opt-in
reasoning_control arms the budget sampler on demand. Router and single
model. Minimal WebUI button as a skeleton for further UI work.

* ui: track reasoning phase via explicit streaming state

Add isReasoning to the chat store, mirroring the isLoading pattern:
per conversation map, private setter, public accessor and reactive
export. Set from the stream callbacks, true on reasoning chunks, false
on the first content chunk, reset on stream end and resynced on
conversation switch. The skip button now keys off isReasoning so it
shows only during the thinking phase, not the whole generation.

* ui: extract control endpoint and action into constants

Move the chat completion routes, the slots route and the reasoning
control action out of chat.service into api-endpoints and a dedicated
control-actions module. No behavior change, drops the magic strings so
the control protocol has a single source of truth.

* server: target reasoning control by completion id

Address @ngxson review on the control endpoint.

Switch from id_slot to the chat completion id to avoid a TOCTOU: the
slot can be reassigned between the lookup and the control request, so
matching the live completion (oaicompat_cmpl_id) is safe and a finished
one simply matches nothing. Rename the action to reasoning_end, guard
it on the reasoning_control flag of the target slot, and reduce the
response to {success} with an optional message.

* ui: target reasoning control by completion id

Keep the streamed completion id on the message and post it back to the
control endpoint instead of probing /slots. Drops the slot discovery
and the TOCTOU that came with it. Action renamed to reasoning_end,
response read as {success}.

* server: address review from @ngxson

Move the control fields into task_params and drop the redundant
comments on the control path.

* server: document the reasoning control endpoint

* Update tools/ui/src/lib/types/database.d.ts

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>

* ui: rename cmplId to completionId

Per @allozaur review, clearer name for the streamed completion id.

* ui: wire completion id capture through the agentic flow

The webui streams through the agentic flow, which relayed onModel but
not onCompletionId, so the completion id never reached the message and
the control request was never sent. Relay it through the flow and its
callbacks type, declare id on the chunk type, and log an explicit error
when the button fires without a usable id.

* ui: target reasoning control model from the message

The model is a property of the completion, so read it from the streaming
message like the id, not from the model dropdown which is unrelated UI
state. Makes the request self-consistent by construction instead of just
unlikely to drift.

---------

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>

tools/server/README.md

@@ -1244,6 +1244,8 @@ The `response_format` parameter supports both plain JSON output (e.g. `{"type":
 
 `reasoning_format`: The reasoning format to be parsed. If set to `none`, it will output the raw generated text.
 
+`reasoning_control`: Arms realtime reasoning control for this completion so it can be ended early via `/v1/chat/completions/control`. Defaults to `false`.
+
 `generation_prompt`: The generation prompt that was prefilled in by the template. Prepended to model output before parsing.
 
 `parse_tool_calls`: Whether to parse the generated tool call.
@@ -1350,6 +1352,22 @@ The server supports parsing and returning reasoning via the `reasoning_content`
 
 Reasoning input (preserve reasoning in history) is also supported by some specific templates. For more details, please refer to [PR#18994](https://github.com/ggml-org/llama.cpp/pull/18994).
 
+### POST `/v1/chat/completions/control`: Control a running chat completion in real time
+
+Acts on an in-flight completion identified by its `id` (the `id` field streamed back by `/v1/chat/completions`). The request is processed in parallel with the SSE stream, so the client sends it while still reading tokens.
+
+*Options:*
+
+`id`: (Required) The chat completion id to act on. A completion that has already finished matches nothing and the call is a no-op.
+
+`action`: (Required) The control action to perform. Currently the only supported value is `reasoning_end`, which forces the end of the current reasoning block so the model moves on to the final answer. Requires `reasoning_control: true` on the original completion request.
+
+`model`: (Required in router mode) The model name, used to route the request to the right instance. Ignored in single model mode.
+
+**Response format**
+
+Returns a JSON object with a boolean `success` field, and an optional `message` field describing the reason when `success` is `false`.
+
 ### POST `/v1/responses`: OpenAI-compatible Responses API
 
 *Options:*