actions: Replace getsentry/action-github-app-token with custom code (…

…#28507)

It seems likely we're running into getsentry/action-github-app-token#18.

Let's replace it with some custom code that works correctly locally.

Committed via a GitHub action: https://github.com/Automattic/jetpack/actions/runs/3971666153

docs/project.json

@@ -1 +1 @@
-{"generatedAt":1674243289678,"builder":{"name":"webpack5"},"hasCustomBabel":false,"hasCustomWebpack":true,"hasStaticDirs":false,"hasStorybookEslint":false,"refCount":1,"packageManager":{"type":"pnpm","version":"7.9.2"},"storybookVersion":"6.5.15","language":"typescript","storybookPackages":{"@storybook/addons":{"version":"6.5.15"},"@storybook/api":{"version":"6.5.15"},"@storybook/builder-webpack5":{"version":"6.5.15"},"@storybook/components":{"version":"6.5.15"},"@storybook/manager-webpack5":{"version":"6.5.15"},"@storybook/react":{"version":"6.5.15"},"@storybook/source-loader":{"version":"6.5.15"},"@storybook/theming":{"version":"6.5.15"}},"framework":{"name":"react"},"addons":{"@storybook/addon-docs":{"options":{"configureJSX":true},"version":"6.5.15"},"@storybook/addon-storysource":{"version":"6.5.15"},"@storybook/addon-viewport":{"version":"6.5.15"},"@storybook/addon-a11y":{"version":"6.5.15"},"@storybook/addon-essentials":{"version":"6.5.15"},"storybook-addon-mock":{"version":"3.2.0"},"storybook-addon-turbo-build":{"version":"1.0.1"}}}
+{"generatedAt":1674253441135,"builder":{"name":"webpack5"},"hasCustomBabel":false,"hasCustomWebpack":true,"hasStaticDirs":false,"hasStorybookEslint":false,"refCount":1,"packageManager":{"type":"pnpm","version":"7.9.2"},"storybookVersion":"6.5.15","language":"typescript","storybookPackages":{"@storybook/addons":{"version":"6.5.15"},"@storybook/api":{"version":"6.5.15"},"@storybook/builder-webpack5":{"version":"6.5.15"},"@storybook/components":{"version":"6.5.15"},"@storybook/manager-webpack5":{"version":"6.5.15"},"@storybook/react":{"version":"6.5.15"},"@storybook/source-loader":{"version":"6.5.15"},"@storybook/theming":{"version":"6.5.15"}},"framework":{"name":"react"},"addons":{"@storybook/addon-docs":{"options":{"configureJSX":true},"version":"6.5.15"},"@storybook/addon-storysource":{"version":"6.5.15"},"@storybook/addon-viewport":{"version":"6.5.15"},"@storybook/addon-a11y":{"version":"6.5.15"},"@storybook/addon-essentials":{"version":"6.5.15"},"storybook-addon-mock":{"version":"3.2.0"},"storybook-addon-turbo-build":{"version":"1.0.1"}}}