Apple TV

You can pause almost anything, since its on demand streaming. By that same token there is no need to record anything either since its on demand, you can stop and start the content at any time you want to.

For things like Sling and cable TV provider’s apps with live TV the app itself would have to offer the DVR option. I know Sling offers DVR on the cloud.

Only if your TV provider app has functionality for that. It is not a system-wide feature of the hardware.

No, Apple TVs are not DVRs they are streaming devices. I would recommend that you study the capabilities of the Apple TV 4K vs a DVR.