[Bug]: Add Custom Emoji: file picker can be opened while form is saving

Before you file a bug report

• I have checked the issue tracker and have not found an issue that matches the one I'm filing.
• This issue is not a troubleshooting question. Troubleshooting questions go here: https://forum.mattermost.com/c/trouble-shoot/16.
• This issue is not a feature request. You can request features and make product suggestions here: https://mattermost.uservoice.com/forums/306457-general/.
• This issue reproduces on one of the currently supported server versions.
• I have read the contribution guidelines and the Mattermost Handbook Contribution Guidelines.

Mattermost Server Version

10.12.0

Build hash: abbf01b9db45d1850eaf3701ea8362b910193ffd

Operating System

MacOS

Steps to reproduce

1. Click on emoji
2. Select Custom Emoji.
3. Click Add Custom Emoji.
4. In the DevTools, set Network to a slower profile to simulate latency.
5. Enter a valid emoji Name.
6. Click Select and choose an Image.
7. Click Save.
8. While the form is saving, try clicking Select again and confirm that the file picker opens.

Expected behavior

The file input should be disabled during save:

• No file picker should open.
• Previously selected image should remain locked in place.

Observed behavior

• The file picker dialog opens while the form is saving, allowing the user to change or remove the image mid-submit.
• This can cause issues on slower networks.

Additional Information

https://github.com/user-attachments/assets/a8dbd1be-05f1-41ae-aca8-fb969da61195