Mattermost-server: Searching in the Emoji Picker should retain search terms when switching to the GIF picker

[mattermod]

Steps to Reproduce:

1. In Mattermost, make sure you have the GIF picker enabled in the System Console.
2. Open the emoji/GIF picker from the center channel.
3. Enter a search string for an emoji that does not exist.
4. Click the GIF tab.

Expected: Search string appears in search box for GIF tab, and GIFs are filtered with that string.
Observed: Search string disappears and you have to re-enter it to find a GIF.

We will need to store the state of the input to those pickers in a common component (probably EmojiPickerTabs) and then propagate that state down through the picker components so that they may share the same variable.

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JIRA: https://mattermost.atlassian.net/browse/MM-23270

[ebaker]

hey, I'd like to work on this 🙂