I see, Supercruise is actually not fixed capability. A lot of the teen series fighters have some supercruise claims at certain conditions.
For example in this interview a former Hornet pilot says that in certain conditions the A model bug can do it. https://youtu.be/y-a-CL8ClX8
I also personally know a Viper pilot who said that in a cold day with 2 wingtip sidewinders and a centerline tank, they can maintain around Mach 1.1 with no AB.
The F-35A also once had a story of maintaining Mach 1.2 with no or minimal AB.
But I think the reason why the manufacturers refuse to call these aircraft Supercruise capable is because they know the capability is too dependent on conditions. (Certain altitudes, cold weather, very little or no load out)
The fact that Saab maintains that the Gripen E is Supercruise capable might suggest that they are confident in capability of the aircraft to Supercruise in a wide set of altitudes, load out configurations or scenarios. Because if it can't, it may tarnish their reputation in their claims.
Hopefully it can, I think the Gripen E is a solid competitor in the lightweight fighter market, competing against the F-16V, J-10C, Tejas, JF-17 etc.