Stylebook: add the Appearance -> Design submenu through admin_menu action

[fushar]

What?

This PR is an improvement to #66851.

Some plugins are triggering the admin_menu action directly to populate the admin menus of a site. Here, I am proposing that we add the Appearance -> Design submenu via that action instead of admin_init.

Testing Instructions

1. Activate a Classic theme.
2. Verify that you still see the Appearance -> Design submenu:

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👋 Thanks for your first Pull Request and for helping build the future of Gutenberg and WordPress, @fushar! In case you missed it, we'd love to have you join us in our Slack community.

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[fushar]

cc: @youknowriad @jasmussen

[ramonjd]

Thank you for updating this. LGTM

Changes to PHP files need a backport reference.

It looks like @tellthemachines has already got a draft up at so you could use WordPress/wordpress-develop#7865 as the backport reference.

Basically, it means adding this PR's URL to the existing md file: https://github.com/WordPress/gutenberg/blob/trunk/backport-changelog/6.8/7865.md?plain=1

After that, I think it's good to go 👍🏻