Hello. Let me try to correct you.
1- Rafale has not be designed to be an air superiority fighter "only".
When France start the programme Rafale, they have multiple needs. Navy need to replace immediately its very old F8 Crusader. They didn't had any fighter able to fight in the air. Only the Super-Etendard which was a quite good attack aircraft. But in the same time, French Air Force had the Mirage 2000, which was an incredible interceptor. But they didn't had a good air to surface attack plane. when the programm was officially launch in 1988, they didn't have a real all time attack fighter. At this time, only Jaguar mainly. They also need to get a fighter able to take the role for nuclear deterrence, which require a fighter aircraft able to penetrate deeply inside ennemy territory.
So, basically, they needed a fighter able to do ANYTHING ! not Air2Air only, and not even secondary A2G capabilities. It was a main concern of the specifications.
This is impossible to achieve. The Rafale is a jack of all trades, a master of none, which is why it sits between the F-22 and F-35 in terms of performance.
It was designed as an air superiority fighter, but some of its design also catered to strike and carrier performance. The end result is the Rafale is not the best ASF, not the best strike fighter and nor is it the best carrier fighter. But the Rafale can do all these things with compromises in aerodynamic design.
The Rafale has inferior supercruise, climb and acceleration performance compared to the F-22 at high altitude, and has only 5.5G and subsonic performance with large payloads at sea level versus the F-35A's ability to go supersonic and have 9G performance with large payload and internal fuel. This is a product of compromise in exchange for versatility. One jet that does everything versus many jets capable of doing one thing best. The former is more important to small air forces or poor countries because we have to manage costs, while the latter is more important to rich superpowers with deep pockets.
2- F-35 is cover by the F-22 in the USAF, it is true. But F-35 has been designed to replace the F-16 in all its major roles. F-35 is not an attack airplane with secondary A2A capabilities. Otherwize it should have been nammed as A-35 instead of F-35. (you can ask : what about F-117 ? But there is an explanation)
It's the aerodynamic qualities that matter. The F-35 is a multirole aircraft, so it can't get an A designation. To get A designation, you must have zero A2A capability. When it comes to aerodynamics, the F-35 has been designed for low-medium altitude. It can't compete in the air with a high performance aircraft like the F-22 and Rafale, even the F-15C and Flanker, at high altitude. Aircraft like the F-16 and F-35 lack the high altitude climb performance and acceleration of dedicated ASF with two engines, and that's a terrible disadvantage in a BVR fight.
People think all you need is avionics, but they forget that you need a jet capable of performing BVR and anti-BVR tactics in the air to actually fight.
3- not completely untrue but I would like to be more specific. The F-35 today is not fully developped yet. Maybe it will arrive in 2029/2031 with block 4/TR3 with very good abilities within air to ground missions. But in the same time, Rafale will be at F5 standard.
Maybe in terms of electronics both will be a match, or both may have different sets of advantages and disadvantages. But I believe the engine upgrade on the F-35 will be a pretty big deal.
For example, the F-35A may have a 20-30% range advantage on internal fuel over the Rafale today, but this could climb to 60 or 70% with a new engine. It will obviously enhance low altitude performance even more than it is today. With the extra range, the ability to go supersonic at low altitude and the ability to retain its payload when challenged due to IWB (the Rafale has to abandon its payload when challenged), the F-35 can run away and try again in the same sortie, and this time the enemy could be unprepared to challenge the F-35, whereas for Rafale it would be a mission kill and a complete waste of time. This is a very serious generation difference.
The F-35 already has some of these advantages today, but the difference between the Rafale and F-35 will widen a lot by the end of the decade.
I don't think we will see a direct competitor to the F-35 in the strike role in the next 20 years.
The F35 have for itself two major capabilities which made him a very good aircraf : VLO and Huge set of sensors associated with data fusion.
The fact is the F35 and Rafale are verry similar in their concept. But Rafale is on continuous development, evolving quite without any limit, and set of sensors and data fusion will be very similar.
If we cannot consider Rafale as VLO, we can anyway consider it as LO fighter (you remind it yoursel, and it is true) . The passives caracteristics that help the F-35 to be VLO will be outdated when it will arrive fully operationnal in some years. Why ? Because all the sensors evolves also (Radar and optronics). So in some times, the VLO caracteristics advantage will decrease a lot.
The Americans are also developing active stealth capabilities for their jets. New digital antennas are being developed for EW suites that are capable of transmitting and receiving. For example, a lot of the receive-only antennas on the F-35 and Rafale can be replaced with these new antennas which can further contribute to active cancellation.
The French may have deployed this capability first, but it doesn't mean others cannot catch up. We could enter the 2030s with active stealth in pretty much all 4.5th and 5th gen and higher jets in varying degrees.