Speed, detection, rockets
We have all seen Tom Cruise redlining his fighter, the metal under tension, going straight into the danger zone. Both Top Gun and Top Gun: Maverick return us to the romanticism of the dogfight, where close quarters combat between fighters takes the uttermost skill and any mistake, or simply just 99% means death.
And it is completely fiction. In the second one they remedied this problem in part by focusing on flying a certain path. You might have heard that the new JSF plane is dog shit in dog fights compared to previous generation Russian and Chinese planes. This is absolutely true. The reason? If your plane needs to dog fight, something has already gone horribly wrong.
Against what games and other media tell you, much of military technology is about making it as easy as possible to kill, regardless of skill. That makes even your substandard grunt able to use a shoulder fired rocket launcher to blow up tanks. With modern planes this is no different. The idea is that the enemy is detected even over the horizon, far beyond what you can see. The plane is purely used as a flying missile launcher, able to quickly reposition if needed. In an ideal scenario they fly out, fire x missiles, get x kills, and they return to base while never having seen more than a few angry dots on a radar. Dog fights should not occur.
SR71
To get a more accurate picture, let us look at the fastest (confirmed) plane in existence. The SR71 Blackbird. It is only exceeded by the X15 and ither X variant prototypes. The SR71 used a few things to its advantage. It had one of the first forms of stealth. It flew so high it was inconceivable for those times that anything did fly there. If it would be detected, there was practically nothing that could reach that high, let alone catch up with the blistering speed.
As the plane is already a pressurised tube to protect the people inside, it shouldn't have too much alterations to fly towards space. However we can look at the X15 for further information. This wasn’t necessarily a practical plane, as it used rockets for it's short flight and most X variant planes needed to be launched from another airplane. This plane could reach the edge of space. Though I can't find much about the materials used, it likely is using much of the same materials as the SR71. You can incorporate designs of both for a plane that can cuise higher, possibly using rockets for periods of flying roughly 80+ km and higher.
And do we need to think of more? These seem to be an all round description of what you need. A modern version of the SR71 blackbird.
For detection you can have specialised planes that do only that, and might not fly high and fast. Alternatively you put a lot of detection technology in your new plane do it mostly for itself. In addition, it'll be embedded in a world wide communication system, so the planes can communicate any position and target as quick as possible to each other and command.
Be a new type of fast and stealth. Technology like ramjets, envelope marerial and aerodynamics have gine leaps and bounds, squeezing ever more performance for speed and stealth.
Have a few special ways to have any payload inside the plane, and a special way to launch them so the plane doesn't tear itself apart when something opens on the plane. My amateur bet would be to simply open a tiny door in the back of the plane, throw out the rocket and activate the rocket a bit later. Experts probably have better solutions to deploy payloads at those speeds, which is a hazard all by itself.
There you have the new fighter. It can detect enemies and communicate it to another plane if they already overshot it. They are so fast practically nothing can take them down. They fly so high they can go into space temporarily, until the lack of atmosphere pulls them back. They are stealth to make detection as difficult as possible. They are basically gone from enemy airspace before they know it, only seeing some ordinance hit home out of nowhere.