The old emote system is slowly being transformed into the new Sticker system. The idea behind Stickers is to allow for custom emoji, custom gifs, custom HTML inserts (e.g. could insert a video via sticker tag if you want), and more. Below is current progress on the new Stickers selector.
Migration of the old emotes system into the new stickers system will be applied automatically on install so existing installs won't lose any custom emotes. The above is what that'd look like.
Stickers come with categories as well so everything can be categorized. The search bar will let your users filter the stickers by their sticker tag. Sticker history is also being implemented to keep track of previously used stickers so users can quickly reuse their favorites. Sticker history, like emoji history, will be entirely handled browser side.
Both categories and stickers have access permissions allowing for giving users new stickers based off permissions. If they use a sticker they're not authorized to use it simply replaces to an empty string so no cheating the system!
Most of the above is just concept and only working roughly 40%, but I expect it to be finalized next week. After this is a redesign of Reactions (GIFs) to support Giphy and Tenor for GIF sources. They'll be designed to no longer be some goofy ugly select list, but with categorization, favorites system, searching, and advanced caching to massively speed up the usage of reactions.