Hi Erin, welcome to the community!
From my research and testing, it appears that label edits - for example adding and removing labels to cards are not tracked in the card activity. There is an open feature request to improve this, and I have passed on your feedback by adding this thread to the ticket.
Our API does allow third-party developers to interact with these action types - https://developer.atlassian.com/cloud/trello/guides/rest-api/webhooks/#webhook-actions-and-types - so you could potentially reach out to a Solution Partner to see if they might be able to create something that enables you to track this: https://partnerdirectory.atlassian.com/.
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