The DNN file manager updates the file/folder listings on a scheduled basis, I believe default is 1 hour. However, you should be able to resynchronize the file manage manually by clicking on the “synchronize” button.

I'm not yet sure where is the issue exactly but the problem comes from the .template extension not being an allowed extension in host settings. If you add the extension there and sync again all will work.

You can enable it temporarily, sync and then remove the extension. At least you will be able to get the existing templates listed.