Deform a hole on a torus

Another geometric option:

Start in the flat, giving a plane a couple of shape-keys, expanding the size of a deleted inset face.

Using a Subdivision > Simple, and 2 Simple Deform > Bend modifiers, bend the plane into a torus.

Now, sliding between the shape-keys will increase the size of the rectangular window.

Here's a shader-only option, using Blender's default UV unwrap of a torus, and keyframing the threshold Less Than values in the following tree:

This can be done by building the torus from 8 different vertex objects, each with 2 Screw modifiers.

One Screw modifier for making a circular section of the torus, and another one to rotate or loop this circle around a center (with an offset) thus creating a torus. The torus turning into 2 rings, and the 4 corners of the hole, warrants the total number of vertex objects and modifiers.

Linking the Screw modifier Angle values with drivers allows a single Angle value to deform the torus.

Making the inverse of this was my starting point so all the drivers are linked to a modifier on the initial vertex I used to make this. In hindsight a bit of a weird place but it works just the same. (So changing the Angle value of the top modifier on the "Vert" object makes it all move.)

I intent to elaborate on this solution a bit when i have more time (especially if you are new to Blender, drivers might take some explaining), but in the meantime...

...Here is the file:

And here is another file utilizing Mirror modifiers on only (and reducing the number to) 2 vertex objects: