[web] Style "Emoji" tab of EmojiAvatarSelectionModal

Summary:
Here's how it looks:

Here it is w/ some "debugging" guides:

Depends on D8287

Test Plan: NA, see above

Reviewers: ashoat, ginsu, rohan

Reviewed By: ginsu

Subscribers: tomek

Differential Revision: https://phab.comm.dev/D8289