Use the sidebar to navigate the Apple TV app - Apple TV box user guide - Apple Support
The described “Channels and Apps” features are for the Apple TV app on the Apple TV box.
Not all apps can connect to the Apple TV app. E.g. Netflix chose to not participate in this, and is therefore not supported for this. Just open the Netflix app directly from the Home Screen. Apps that have been programmed with this support, can connect (or changed to not connect) by user settings: Settings﹥Apps﹥TV app﹥[ᴄᴏɴɴᴇᴄᴛ ᴛᴏ ᴛᴠ]﹥{app name}﹥On|Off.
I suppose the sidebar is supposed to list channels and supported apps that the user is actually watching content from via the Apple TV app, making the list manageably short. The sidebar listing is a bit less than a shortcut to the app, instead it brings a subset of content into the Apple TV app (Up Next content and a few popular/recommended shows).
Use the sidebar to navigate the Apple TV app - Apple TV app user guide for third party devices - Apple Support
External apps wouldn’t connect on third party devices with the Apple TV app, as the ‘connecting’ is done through the operating system on select Apple devices.
My sidebar is missing the Channels & Apps List. It actually stops at the Library.
Try searching for a Hulu/Prime/Peacock show in the Apple TV app, then Add it to Up Next, and initiate playback from within the Apple TV app. Maybe that triggers it?
Else not sure how that would happen. If the issue persists, then I would suggest to contact an expert from the Apple Support staff for further assistance. Contact Apple for support and service (phone numbers) or start your support request online (chat/email/callback).