fix(js_run_devserver): ensure files are synced before waiting for next build event

[jbedard]

I think this removes the possibility of processing multiple build events in parallel.

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Changes are visible to end-users: no

Test plan

• Covered by existing test cases

[aspect-workflows[bot]]

Test

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e2e/bzlmod

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e2e/npm_translate_lock

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e2e/npm_translate_lock_partial_clone

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e2e/npm_translate_lock_replace_packages

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e2e/npm_translate_lock_subdir_patch

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e2e/npm_translate_package_lock

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e2e/npm_translate_yarn_lock

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e2e/package_json_module

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e2e/pnpm_lockfiles

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e2e/pnpm_workspace

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e2e/pnpm_workspace_rerooted

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e2e/repo_mapping

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e2e/rules_foo

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e2e/runfiles

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e2e/vendored_node

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