I'm not sure on Core, either. I looked for a gnome-extension that would emulate the App-Drawer function that Mate Desktop has but came up empty-handed.
You may also try searching for a gnome-extension that serves this (with more patience than I, and may have more luck).
Zorin OS Lite does offer this function.
On Zorin OS Lite, this can be achieved by creating a panel launcher, then adding your preferred applications to it. This will create a grouped list with an Arrow Icon.
It does make a difference which desktop environment you are using; The different desktops all have their pros and their cons and offer a lot of diversity in how they operate. This diversity is a very enjoyable thing and a user can gain a lot by exploring them.