fix: replace raw string type literals with protocol.Type* constants in mixed-mode chat

[clubanderson]

Closes #3832

Summary

• Added four new protocol.MessageType constants to pkg/agent/protocol/messages.go: TypeStreamChunk, TypeStreamEnd, TypeMixedModeThinking, and TypeMixedModeExecuting
• Replaced all 9 bare string literals ("stream_chunk", "stream_end", "mixed_mode_thinking", "mixed_mode_executing") in handleMixedModeChat with the corresponding protocol.Type* constants

Test plan

• go build ./... passes
• Verify mixed-mode chat still works end-to-end (message types are unchanged at the wire level since the constants resolve to the same string values)

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• 511e1a0 fix: replace raw string type literals with protocol.Type* constants in handleMixedModeChat (Mixed-mode chat uses raw string type literals #3832)

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[Copilot]

Pull request overview

This PR standardizes mixed-mode chat WebSocket message typing by replacing raw string type literals with shared protocol.MessageType constants, reducing the risk of silent protocol drift between layers.

Changes:

• Added protocol.TypeStreamChunk, protocol.TypeStreamEnd, protocol.TypeMixedModeThinking, and protocol.TypeMixedModeExecuting.
• Updated handleMixedModeChat to use the new protocol.Type* constants instead of bare string literals.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated no comments.

File	Description
pkg/agent/server.go	Replaces mixed-mode WebSocket message Type fields from raw strings to protocol.Type* constants.
pkg/agent/protocol/messages.go	Introduces new MessageType constants for mixed-mode phases and stream chunk/end events.