Is there an IPTV Player with the ability to conveniently rewind the air and timeshift?

Question

A television

Hello!
I am spoiled by the capabilities of the Beeline TV set-top box. Now I want to expand the capabilities of my home media system. I want to put a monitor and a computer instead of a TV-a (s) and get everything the same on it.
The recording of the broadcast and the timeshift itself are almost everywhere, but with rewinding the broadcast it’s as convenient as Beeline’s (MS Mediaroom) has never seen. It works like this: as soon as you turn on any channel, its background recording immediately starts. And while watching, it is possible to wind the air back up to the moment you switched to this channel. And forward to the real (live) broadcast (Live). Accordingly, a pause anywhere. (But the recording let us down. If the transfer is over, then regardless of the fact that you can watch it in "rewind", you cannot save it to disk. But this is Beeline's sadness). Moreover, there is no transition from timeshift / rewind to "Live", i.e. you move the air forward, you stumble upon Live - you just immediately look further on the "live" air. Probably messy to describe.
Here I want the same, but on the computer. The operating system is not very important. The main thing is that the player should be comfortable.
If who such met - tell please.