The download is quite subtle in the TV app interface. The download-from-cloud symbol changes into a checkmark, when started, but that is only visible if you hover over the right tile. The Activity window will show progress, but that is hidden until you bring it up. A small download-progress indicator spinner (is also a button for the Activity window) would appear between the Library tab and the Search field. After the download is complete, no notification, and now nothing will show where the download-from-cloud symbol or checkmark was when hovering over the tile. After the download is complete, a few contextual changes are visible in the More (⋯) button of that tile (e.g. “Remove download”).
The Rentals category in the side bar can be set to hidden. Try unhiding the corresponding checkbox by editing the sidebar. The Edit button/word/link will appear only when hovering in the sidebar’s top-right corner.
I think this was largely the same from Big Sur (your system) to Monterey (my system). Apologies if I forgot any differences.