Will the pie still be available for use after the festival is over ?
During the afternoon of Loredas, 6 Sun’s Dawn 2e578 a big piece of Aetherius fell to Nirn. It was the first major piece of Aetherius to fall on Nirn in more than five hundred years. It scattered around the world as millions of shards. It was rapidly documented by Lady Cinnabar of Taneth in her pamphlet Aetherial Fragments that "... when three shards meet, they re-form into a silvery prism by unknown process and confer the power unlocked by the merger to a nearby being." The Order of the Black Worm, commonly known as the Worm Cult, reappeared in Tamriel shortly thereafter and some of its members are avidly searching said shards.
In the last week of First Seed 2e579, an arcane explosion occurred in the Imperial City — a night of storms, and trembling terrain. They named it the "Soulburst". That day Emperor Varen Aquilarios disappeared without a trace. His wife, Clivia Tharn, ascended to the Ruby Throne as Empress Regent under the guidance of the Necromancer Mannimarco. Ushering a time of increased instability within the Empire of Cyrodiil which finally grew into “The Three Banners War”.
As far as it giving the Experience Bonus, I doubt it. It will probably do the same thing as the Witchmother's Whistle Memento we received from one of the last Festivals and just have an animation.
I doubt they will remove it from your Collections since it will be needed at the Jester Festival next year.