I have recently purchased a disk copy of the original Minecraft Xbox One Edition (because in my opinion it's better than today's Minecraft) and I haven't put it in my Xbox yet because I am too afraid that it will update to the latest version. (If it helps, I already own a digital copy of Minecraft Bedrock that came with my Xbox).
It should prompt you to download the update first. You can then choose the option to not install the update. If you click download, however, there should be an option to cancel the update, like pressing B. I do not recommend that though, as it might corrupt some data. I learned that the hard way.
I don't own an Xbox One so this might not be how it works, but this is how it worked in Xbox 360, so this is (hopefully) accurate.
For PS4 Edition, once they become Bedrock Edition, you can click "Editions" to play the PS4 Edition. That is the easiest way to access your PS4 Edition exclusive stuff (i.e. Battle, Tumble, and Glide Mini Games) whilst having updated to Bedrock Edition. Xbox One Edition and Minecraft Bedrock (on the Xbox One) are separate games. However, you cannot find Xbox One edition on the Microsoft store.