Is there a way to update user data in the UI?

I'd like to update the user data object in the UI. I know I can do it via the API: https://fusionauth.io/docs/v1/tech/apis/users

Not currently. If you are interested in doing so, please file an issue https://github.com/FusionAuth/fusionauth-issues/issues

There are a few open issues that may cover your use case as well, feel free to comment, upvote and add details about your use case.
https://github.com/FusionAuth/fusionauth-issues/issues/213
https://github.com/FusionAuth/fusionauth-issues/issues/485

If you use the advanced registration forms, you can edit user data now. This was recently released as a premium feature (requiring a paid license; more info here).

More info on setting up the user data editing screen: https://fusionauth.io/docs/v1/tech/guides/advanced-registration-forms/#editing-user-data-in-the-admin-ui