This is not possible, as shopify uses "only" tags for their filter options in general.
What you could do is use some sort of "auto-tagging" app or if you use shopify plus you can use Flow.
Everytime a product gets created /or published - create a tag using the Product Type. This way you can automate it. Or if you can't do that then you simply download all products - and then simply create a tag using Product Type column.
Lets say Product Type is in Column A and Tags in Column B - Then you would create another column next to B: Temporary Tag:
then in column C write: =A2 (pull it down) to the bottom of the file.
Now you need to merge column "B" where tags are already with column C (temporary column). Simply create another column D and write in there: =B2&","&C2
This should then merge the column into one - mark the column and copy paste "Values only" into the tag column. Delete the temporary columns, upload the csv file and now you should have all products also tagged with "product type".