Add routing_method experiment variable for A/B/C hydra experiment

[bhavyaus]

Port of microsoft/vscode-copilot-chat#4947.

Summary

Add copilotchat.autoModeRoutingMethod ECS flight variable to control which routing algorithm the auto-intent-service uses per-request. This enables A/B/C experiments for the HYDRA model router.

A/B/C Experiment Design

Path	Value	Behavior
A	'' (empty, default)	Production automod — no router call
B	'binary'	Binary classifier v1 (current router)
C	'hydra'	HYDRA multi-head capability matching (new)

Fallback for B/C → automod (path A), signaled via fallback=true in the response.

Changes

• configurationService.ts: New AutoModeRoutingMethod experiment-based setting
• routerDecisionFetcher.ts: Add routingMethod param, send routing_method in request body, extend RouterDecisionResponse with new fields
• automodeService.ts: Read experiment var, handle fallback=true responses

[github-actions]

Screenshot Changes

Base: fc99d59e Current: 8b35d402

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[Copilot]

Pull request overview

Adds an experiment-driven “routing method” selector for Auto Mode’s model router integration, enabling the auto-intent-service to vary its routing algorithm per request (e.g., binary vs hydra), and handling server-signaled router fallbacks.

Changes:

• Introduces chat.advanced.autoModeRoutingMethod as a team-internal, experiment-based setting (ECS: copilotchat.autoModeRoutingMethod).
• Sends routing_method in the router request body and extends the router response type to include fallback/hydra-related fields.
• Handles fallback=true router responses in Auto Mode by falling back to default model selection and logging the fallback reason.

Show a summary per file

File	Description
extensions/copilot/src/platform/endpoint/node/routerDecisionFetcher.ts	Extends router response typing and adds routing_method to the request + extra trace logging.
extensions/copilot/src/platform/endpoint/node/automodeService.ts	Reads the experiment variable, forwards routingMethod to the router, and handles router-signaled fallback behavior.
extensions/copilot/src/platform/configuration/common/configurationService.ts	Registers the new experiment-based config key for selecting the routing method.

Copilot's findings

• Files reviewed: 3/3 changed files
• Comments generated: 4