feat(webserver): customize shutdown with new kill option

[Skn0tt]

We had this change up earlier, but it staled because I was unsure what PID to signal. After doing some more research on it, it appears that both for SIGINT and SIGTERM it's appropriate to send to the entire process group. So this PR is a reopening of #33379 with those learnings.

Closes #33377, #18209

[github-actions]

Test results for "tests 1"

1 failed
❌ [webkit-page] › page/page-leaks.spec.ts:161:5 › waitFor should not leak @webkit-ubuntu-22.04-node18

4 flaky

⚠️ [firefox-page] › page/page-evaluate.spec.ts:403:3 › should throw for too deep reference chain @firefox-ubuntu-22.04-node18
⚠️ [playwright-test] › ui-mode-test-output.spec.ts:80:5 › should show console messages for test @macos-latest-node18-1
⚠️ [chromium-library] › library/popup.spec.ts:264:3 › should not throw when click closes popup @ubuntu-20.04-chromium-tip-of-tree
⚠️ [playwright-test] › ui-mode-test-watch.spec.ts:145:5 › should watch all @windows-latest-node18-1

37414 passed, 654 skipped
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Merge workflow run.