pause apple tv in Spectrum app?

Any functionality of the Spectrum TV app is the responsibility of the Spectrum developers. Inquire with them.

Rewinding requires the “Cloud DVR” option added to your plan, and watching a recording (not live TV). Do you have that?

Spectrum TV app: Download and get started - Spectrum Support

Spectrum TV app on Apple TV - Spectrum Support

Cloud DVR (cDVR) and Cloud DVR Plus FAQs - Spectrum Support

FAQs

Q5: Can I rewind live TV or transfer my recordings?

A5: No. The closest thing that can be done on live TV is setting an in-progress recording.

^ This applies to their app on any device, not specific to Apple.

(I have Spectrum with my AppleTV) To reiterate Urquhart’s correct answer, and to answer your latest post, to pause live TV with Spectrum, yes you will need a DVR capable cable box.

The links to Spectrum were provided, you definitely want to use them to take your question to Spectrum. They can give you detailed information that Apple support won’t have.