fix: use lvt/testing client library in chat example

[adnaan]

Summary

• Replace custom serveClientLibrary function with e2etest.ServeClientLibrary from lvt/testing package
• This ensures the chat example uses the same embedded client library as other examples
• Fixes CI test failures in cross-repo tests where the client couldn't be found

Root Cause

The chat example had a custom serveClientLibrary function that looked for the client in local paths:

• livetemplate-client.js
• ../client/dist/livetemplate-client.browser.js
• ../../client/dist/livetemplate-client.browser.js

But the CI workflow copies the client to lvt/testing/livetemplate-client.browser.js, which is then embedded via go:embed in the lvt/testing package.

Test plan

• Build passes locally
• CI tests pass

🤖 Generated with Claude Code

[Copilot]

Pull request overview

This PR replaces the custom serveClientLibrary function in the chat example with the standardized e2etest.ServeClientLibrary function from the lvt/testing package. This change ensures consistency with other examples and fixes CI test failures where the client library couldn't be found at the custom paths.

Key Changes:

• Removed custom client library serving logic that searched multiple local paths
• Added dependency on github.com/livetemplate/lvt/testing package
• Updated to use the embedded client library via e2etest.ServeClientLibrary

Reviewed changes

Copilot reviewed 2 out of 3 changed files in this pull request and generated 1 comment.

File	Description
chat/main.go	Replaced custom serveClientLibrary function with standardized e2etest.ServeClientLibrary import and usage
chat/go.mod	Added github.com/livetemplate/lvt dependency to support the new client library serving approach
chat/go.sum	Updated checksums to include the new lvt/testing dependency

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[Copilot]

The version of github.com/livetemplate/lvt being added (v0.0.0-20251213063335-769e058d10cd) is newer than the versions used in most other examples. For consistency, consider using the same version that other examples use (v0.0.0-20251130141940-9b94cde94e9d as used in counter, avatar-upload, and todos examples), unless there's a specific reason this example requires a newer version. Version inconsistencies across examples can make maintenance more difficult and may lead to unexpected behavior differences.

Suggested change

	github.com/livetemplate/lvt v0.0.0-20251213063335-769e058d10cd
	github.com/livetemplate/lvt v0.0.0-20251130141940-9b94cde94e9d