[browser] fix corerun

[pavelsavara]

• improved CI path evaluation
• added runtime asserts for internals and runtimeApi objects
• fixed merging
• set DOTNET_SYSTEM_GLOBALIZATION_INVARIANT

[dotnet-policy-service]

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[Copilot]

Pull Request Overview

This PR fixes issues with corerun in the browser environment by ensuring proper initialization of the RuntimeAPI object across multiple native modules. The changes address scenarios where the RuntimeAPI might be undefined, which could cause runtime failures.

Key changes:

• Adds defensive initialization of RuntimeAPI objects in native modules
• Updates pipeline configurations to properly handle WASM CoreCLR runtime tests
• Adds eslint disable directive for unused variable warnings

Reviewed Changes

Copilot reviewed 7 out of 7 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
src/native/libs/System.Runtime.InteropServices.JavaScript.Native/interop/index.ts	Adds defensive initialization for RuntimeAPI object before assignment
src/native/libs/System.Native.Browser/utils/index.ts	Adds defensive initialization for RuntimeAPI object before assignment
src/native/libs/System.Native.Browser/libSystem.Native.Browser.extpost.js	Adds defensive initialization and eslint disable directive
src/native/corehost/browserhost/host/index.ts	Adds defensive initialization for RuntimeAPI object before assignment
eng/pipelines/runtime.yml	Updates pipeline condition to include new WASM CoreCLR runtime test path variables
eng/pipelines/common/templates/wasm-runtime-tests.yml	Updates path variable reference from generic to mono-specific
eng/pipelines/common/evaluate-default-paths.yml	Adds new WASM CoreCLR runtime tests subset and updates path configurations

[radekdoulik]

LGTM

[pavelsavara]

I filled #120317