Hi @Chase.MESH,
In Webflow, Archived doesnt mean deleted, it just means not active.
Only way to truly remove these items from search results without custom code would be to delete them.
Even with Google Email, when you archive an email it is not truly deleted until you DELETE the message.
Hope that answers your question. As I mentioned though, you should be able to do this with some custom code. And I did find an older post relating to your question a bit. Questions about archived CMS items - #2 by cyberdave
To remove them from search and view you might need to reach out to Webflow Customer Support and have them remove the archives from the cache. At least that is what I am interpreting from that older post. Not sure if that is still the case 2 years later. @cyberdave you have any thoughts on this, since you did write the response to it?
Happy Designing,
Brandon