Hi Chad Weber,
I'm glad to know that the asset was deleted from the Data Catalog and thank you for posting your solution so that others experiencing the same thing can easily reference this! Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I am reposting your solution in case you'd like to "Accept " the answer.
Issue: Asset still exists even after being deleted from the Data Catalog.
Solution:
It took a few hours for the Data Catalog to show that the asset was deleted. Purview takes a while to update the Data Catalog.
If I missed anything please let me know and I'd be happy to add it to my answer, or feel free to comment below with any additional information.
I hope this helps!