You would need to use an exists statement for this and be reasonably familiar with navigating the API explorer for code names (using the reference and collection tabs). You can read up on exists filters here:
https://experienceleague.adobe.com/docs/workfront/using/reporting/reports/text-mode/create-complex-text-mode-filters-using-exists-statements.html?lang=en
The API explorer is here:
https://developer.adobe.com/workfront/api-explorer/
Taking the following as a sample of code you would add to a project report:
EXISTS:a:$$OBJCODE=DOCFDR
EXISTS:a:projectID=FIELD:ID
EXISTS:a:$$EXISTSMOD=NOTEXISTS
EXISTS:a:name=Archive
EXISTS:a:name_Mod=cicontains
This code is saying
1. For any folder...
2. ...where the folder's project ID is the same as the ID on your project report (i.e. the project's ID)...
3. ...there does not exist...
4. and 5. ...folders where the name of the folder contains the word Archive
In plain english, your list of projects will contain only folders without the word "archive" in the name.
I used the api explorer to look up the name for the folder object, as well as the fields I would need from that object (projectID and name). It was helpful to see on the folder object that I would be able to reference the project (project ID), but I am mindful that if you added the folder to a task on the template, the code above might need to be amended to look for a task id which would be an interesting challenge in a project report.