Fix Playwright tunnel restart race

[justinTM]

Summary

Fixes #5852.

Fixes a lifecycle race in the Playwright Local Browser Server VS Code extension where a rapid stop/start could create a replacement tunnel before the previous tunnel finished stopping.

The extension now tracks an in-progress stop promise, waits for it before starting a replacement tunnel, and only clears the active tunnel reference after stopAsync() settles.

Commit structure

This PR is intentionally split into a red/green sequence:

1. 39a590c935 - adds the real VS Code host regression test only.
2. d16c95ebb1 - adds the lifecycle fix and change file.

Red/green proof

Both runs used the same command sequence from vscode-extensions/playwright-local-browser-server-vscode-extension:

• PATH=/Users/justin/.cache/codex-runtimes/codex-primary-runtime/dependencies/node/bin:$PATH /Users/justin/.cache/codex-runtimes/codex-primary-runtime/dependencies/node/bin/node ../../common/scripts/install-run-rushx.js build
• env -u GITHUB_ACCESS_TOKEN -u GH_TOKEN -u GITHUB_TOKEN -u GITLAB_ACCESS_TOKEN -u RUNNER_REGISTRATION_TOKEN -u TAILSCALE_AUTH_KEY PATH=/Users/justin/.cache/codex-runtimes/codex-primary-runtime/dependencies/node/bin:$PATH VSCODE_EXECUTABLE_PATH='/Applications/Visual Studio Code.app/Contents/MacOS/Electron' /Users/justin/.cache/codex-runtimes/codex-primary-runtime/dependencies/node/bin/node ../../common/scripts/install-run-rushx.js test:vscode

Red, at test-only commit 39a590c935:

AssertionError [ERR_ASSERTION]: Start resolved while the previous Stop command was still pending.
true !== false
Exit code:   1
RED_EXIT=1

Green, after fix commit d16c95ebb1:

Playwright tunnel restart remained pending behind the in-progress stop.
Exit code:   0
GREEN_EXIT=0

I also ran git diff --check origin/main...HEAD on the final branch.

Notes

The test:vscode script launches a real VS Code extension host against the built dist/vsix/unpacked extension using @vscode/test-electron. It runs a focused rapid Start/Stop/Start assertion that verifies restart remains pending while the prior Stop command is still in progress.

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