If you've bought templates from klasspaperless.com, you can see and send every one of them right from inside Klass-RM Uploader - no downloading a file or unzipping an archive first. Available on Mac and iOS/iPadOS.
Signing in
This uses a separate Klass account from your reMarkable sign-in - the account you used to check out on klasspaperless.com, not your reMarkable login. Look for the Store section in the app and sign in with your Klass Paperless email.
Sending a purchase
Once signed in, every template you've purchased is listed in the app. Tap or click a template to download it, and tap or click Send to upload it straight to your reMarkable in one step.
Browsing, downloading, and sending are not gated by a Klass-RM Uploader license or a reMarkable Connect subscription - with one exception, below.
The custom-template exception
If a purchase is a custom reMarkable template package (.rmtemplate), the same rule that applies to any custom template applies here too: your reMarkable account needs Connect with Methods for the tablet to let you actually select it. If your account is not eligible, the Send row shows a lock and a short explanation (or, while the app is still checking your account, a neutral "Checking your reMarkable account..." message) - but Download stays available either way, since you own the file regardless. See the Custom reMarkable Templates page for the full picture.
A .rmtemplate was never previewable in-app to begin with, since there is no PDF preview for a template package.