fix(coding-agent): preserved btw codex websocket routing

- Preserved the session websocket preference for ephemeral /btw side-channel turns so Codex websocket-only models do not fall back to SSE.
- Prioritized active /btw and /omfg panels in Esc handling before loop, maintenance, and main-turn interrupts.
- Added regression coverage for side-channel websocket options and /btw Escape priority.

Fixes #5213

packages/coding-agent/src/modes/controllers/input-controller.ts

@@ -266,6 +266,8 @@ export class InputController {
 			});
 		}
 		this.ctx.editor.onEscape = () => {
+			// Side-channel panels are the topmost view. Esc dismisses them before
+			// touching loop mode, maintenance, or the underlying main turn.
 			// Active context maintenance owns Esc: auto/manual compaction,
 			// handoff generation, and auto-retry backoff all advertise
 			// "(esc to cancel)". Dispatch on live session state instead of
@@ -281,6 +283,13 @@ export class InputController {
 			// (see EventController). Main-session maintenance still owns Esc and
 			// stays cancellable from the main view (focused submit gates /compact
 			// and handoff, so manual maintenance is main-only anyway).
+			if (this.ctx.hasActiveBtw() && this.ctx.handleBtwEscape()) {
+				return;
+			}
+			if (this.ctx.hasActiveOmfg() && this.ctx.handleOmfgEscape()) {
+				return;
+			}
+
 			if (!this.ctx.focusedAgentId) {
 				const viewSession = this.ctx.viewSession;
 				let aborted = false;
@@ -308,12 +317,6 @@ export class InputController {
 				}
 				return;
 			}
-			if (this.ctx.hasActiveBtw() && this.ctx.handleBtwEscape()) {
-				return;
-			}
-			if (this.ctx.hasActiveOmfg() && this.ctx.handleOmfgEscape()) {
-				return;
-			}
 			if (this.ctx.focusedAgentId) {
 				// Esc never interrupts the focused agent's turn: clear typed text,
 				// else return the view to the main session. Interrupt via empty

packages/coding-agent/src/session/agent-session.ts

@@ -14706,7 +14706,7 @@ export class AgentSession {
 				// stable, but give provider routing a unique request lineage.
 				sessionId: `${cacheSessionId}:side:${Snowflake.next()}`,
 				promptCacheKey: cacheSessionId,
-				preferWebsockets: false,
+				preferWebsockets: this.#preferWebsockets,
 				reasoning: toReasoningEffort(this.thinkingLevel),
 				disableReasoning: shouldDisableReasoning(this.thinkingLevel),
 				hideThinkingSummary: this.agent.hideThinkingSummary,