At least the mural that Zelda describes doesn't really contradict what we know of the foundation of the Kingdom of Hyrule. That period of time is still extremely vague, what we know of the period between the ending of Skyward Sword and the actual foundation of the Kingdom of Hyrule is minimal. All we have are tidbits from OoT, TP, ALBW, and HH:
- There were years of peace
- Then word of the Triforce spread and that led to an era of chaos. During that era of chaos, one of the many groups that coveted the Triforce were the Dark Interlopers. The Goddesses then intervened and sent the Spirits of Light.
- Chaos continued until Rauru, the Sage of Light, used "powers stronger than both time and the Master Sword" to seal the Sacred Realm away. The Spiritual Stones were then given to their respective tribes.
- Many years later, "the descendants of the Goddess Hylia, who was reincarnated as Princess Zelda, established the kingdom of Hyrule and became Hyrule's royal family."
The only sore points are Rauru being this Zonai and how Ganondorf was there for the Era of Chaos. And yet, that happening does clear up some mysteries left still from OoT, mainly Ganondorf's origin and Twinrova. The 400 year old witches being Ganondorf's surrogate mothers and worshipping him early on as the Demon King (HH page 90) and knowing ritual to revive the Demon King are unexplained to this day. So them fitting the idea of "Twinrova giving some of Ganondorf's Malice a human shell and that is the Ganondorf we know" is not thaaat out there.
Though wherever they go, all we know for certain is that in the past of BotW the events of SS, OoT, and now seemingly ALttP, as the ancient records read by Zelda mix the Imprisoning War with the events seen in the mural, do happen.