Currently,

• Custom emojis are managed at the site level via the emoji admin screen:
  https://<site>.atlassian.net/admin/emoji

• Only Confluence site administrators can add, edit, or delete these emojis.

• When an emoji is deleted, existing references (for example, those described in the KB below) break and the emoji falls back to the text form :emoji-name:.

• There is no corresponding entry in Confluence/organization audit logs that records:

• • Which admin created/updated/deleted an emoji

• • When the change happened

• • Which emoji (name / ID) was affected

Reference KB:
[Custom emojis are not displayed as expected in Confluence page | Confluence | Atlassian Support|https://support.atlassian.com/confluence/kb/custom-emojis-are-not-displayed-as-expected-in-confluence-page/]

There should be a way to track this in the audit logs