Russia has three types of strategic bombers in total if you count the Tu-22M3.
Not really, and if you were being pedantic the Bear and the Blackjack have largely lost their capacity to carry bombs so they are not really bombers at all... they are cruise missile carriers.
The Tu-22M3 is a good aircraft, but it is a theatre bomber... it struggled to reach targets in Syria with bomb loads of 9-12 tons from Russian air bases, so unless you mean flying from the far east and hitting US targets in Alaska then you can't call it a strategic anything.
With the inflight refuelling probe reinstalled its performance should improve, but it still is not a strategic aircraft... more a heavy theatre bomber and missile carrier.
It is a perfectly fine strategic bomber, and younger than most of the competitors out there other than Tu-160M and freshly modernized Tu-22.
Strategic is technically defined as a flight range of 10,000km or more and the Backfire and Tu-16 fail on those counts.
They are useful aircraft, but not strategic.
The same for the C-130 which some called a strategic light transport... but it isn't able to fly strategic distances with any useful payload.
Only it will be possible to strike faster with ICBM or SLBM, but in this case it will be conventional strikes, optionally nuclear.
You can deploy bombers and have them waiting on station for orders to attack. You can call them back if you need to. Can't do that with ICBMs and SLBMs...
But I think the Supersonic speed of the Backfire allows it to move in more quickly to a firing area, giving the enemy less time to react.
Flying at supersonic dramatically reduces the flight range of the Backfire, yet at the same time is not fast enough to make them safe from most ground based air defence. The mach 2 speed of the Backfire would be useful against shit planes like the F-35, but most more capable fighters wont be challenged so much.
Perhaps the stealth capability of the PAKDA will compensate for its lack of speed, I think another factor is how the enemy is able to detect the takeoff of an aircraft in preparation for missile strikes.
The stealth should reduce the distances it can be detected, but it is most likely to be using standoff weapons to evade interception too.
It is also supposed to be able to carry a significant number of air to air missiles to shoot down enemy aircraft that threaten the bomber, but also to shoot down incoming SAMs and AAMs being fired against the aircraft.
Its surprising to know that the Backfire has a slightly higher payload capacity than the Lancer.
That top ordinance weight of the Lancer would only be able to be achieve if they reinstalled the external weapon pylons which they removed for a weapons treaty.
As for my proposal, its not to restart production of the Backfire, but to develop a successor, a supersonic missile carrier of the medium class. (Tu-160 being heavy class while Mig-31/Future Mig-41 being the light class)
Getting to supersonic speeds takes a long time and uses up a lot of fuel and it can't remain supersonic for extended periods unless you change the engines to ramjets.
I would say the MiG-41 is going to need good range and decent internal capacity for air to air missiles and all of that is going to make it rather bigger than the MiG-31 IMHO, so I suspect in terms of subsonic the PAK DA will replace the Backfire as the theatre bomber and the Bear in the role of subsonic long range cruise missile carrier, and the MiG-41 might be in a heavier weight class than the MiG-31 and its internal weapons and ammo and fuel might result in a much bigger aircraft.
Even though the PAK-DA is the official successor to the Tu-22, in reality the MiG-41 will fulfill the functions of both the MiG-31 and Tu-22.
If they need a theatre bomber that is supersonic they should have plenty of Tu-160s around the place, for subsonic theatre bomber and subsonic strategic bomber they will have the PAK DA. To clear the skies of enemy aircraft they will have MiG-31 and MiG-41 interceptors with super long range AAMs. These aircraft operating in an air defence role to deal with enemy aircraft and cruise missiles and bombers, could also be expanded to include drones, while versions of both aircraft carrying hypersonic long range missiles can deal with deep strikes into enemy territory and attacking enemy assets like landing ships and carrier groups etc etc.