Current problem
All emojis are shown based on what guild they are from, animated or static alike, which can sometimes make finding certain ones difficult if you don't know the name of the emoji.
Proposed change
Add a simple toggle or checkbox where you can choose to show if you want to see only static emoji or animated emoji.
Potentially an additional setting toggle for customisation could be considered as well to allow people to choose if they want their filter setting to remain applied when exiting back out of the emoji menu, or if it should show all emoji again the next time the menu is opened.