All of the TV Everywhere apps require some form of Live TV service (cable, satellite, streaming).
As noted for CBS, it depends on what you want to watch. For live sports, you don't have many cheap options. You can get the higher-end Paramount+ with Showtime (ad-free), which gives you a live feed of your local CBS station. But that live feed is just that, live only. No DVR or rewind or anything similar. If possible you can get an antenna and watch for free with your TV. You can also get one of many external tuners that usually have DVR features, too.
Otherwise, it looks like CBS is typically only available with full cable-replacement style services, with their high prices.
Or you can give up on sports, and then just use regular streaming services for "next day".