[deps] Platform: Update @types/chrome to v0.0.306 (#12126)

* [deps] Platform: Update @types/chrome to v0.0.306

* Fix APIs

* Add `await`

* Fix tests

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Co-authored-by: renovate[bot] <29139614+renovate[bot]@users.noreply.github.com>
Co-authored-by: Justin Baur <19896123+justindbaur@users.noreply.github.com>

package.json

@@ -58,7 +58,7 @@
     "@storybook/theming": "8.5.2",
     "@storybook/web-components-webpack5": "8.5.2",
     "@types/argon2-browser": "1.18.4",
-    "@types/chrome": "0.0.280",
+    "@types/chrome": "0.0.306",
     "@types/firefox-webext-browser": "120.0.4",
     "@types/inquirer": "8.2.10",
     "@types/jest": "29.5.12",