I was recently asked how the color of one shape can be changed and for other shapes to be automatically updated to the same color … even if they are on different pages! Well, it is possible with Microsoft Visio’s awesome ShapeSheet formulas. In fact, this capability is not limited to the FillForegnd cell … check out the Microsoft Learn page about SETATREF(…), and view the video below to find out more.

The formula in a ShapeSheet formula of one shape can reference the value of another cell, which can be in a different shape on the same page, or even on a different page.
For example, the formula =Sheet.1004!FillForegnd will get the fill color of the shape with the ID = 1004, and, if this is entered into the FillForegnd cell of another shape, then it will be the same color. This formula could be enclosed in the GUARD(…) function, if you don’t want the color to be changed, or enclosed in a SETATREF(…) function, if you want the color to be updated on either shape to keep them synchronized.
This short video explains how this can be done with the ShapeSheet in Visio …
Of course, it does not have to be limited to the fill color….
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Well written
There is also the three shapesheets —> TheSheet, ThePage and TheDoc.
So you could assign the colour to TheDoc or ThePage.