feat: support partitioned storage state

[yury-s]

Reference #35598

[github-actions]

Test results for "tests 1"

2 failed
❌ [webkit-library] › library/browsercontext-storage-state.spec.ts:369 › should roundtrip local storage in third-party context @webkit-ubuntu-22.04-node18
❌ [webkit-library] › library/browsercontext-storage-state.spec.ts:509 › should set indexedDB in third-party context @webkit-ubuntu-22.04-node18

4 flaky

⚠️ [firefox-library] › library/inspector/cli-codegen-1.spec.ts:1079 › cli codegen › should not throw csp directive violation errors `@firefox-ubuntu-22.04-node18`
⚠️ [firefox-page] › page/page-goto.spec.ts:81 › should work with Cross-Origin-Opener-Policy `@firefox-ubuntu-22.04-node18`
⚠️ [firefox-page] › page/page-wait-for-function.spec.ts:104 › should work with strict CSP policy `@firefox-ubuntu-22.04-node18`
⚠️ [playwright-test] › ui-mode-trace.spec.ts:637 › should indicate current test status `@ubuntu-latest-node24-1`

46658 passed, 805 skipped

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Merge workflow run.