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I want to add a caption to an equation, the suggestions by previous "experts" in this forum are wrong. This used to be a very simple operation but it is no longer. Users used to be able to add a caption to an equation that was right justified along the margin at the same horizontal level as the equation by merely clicking "add caption". Now, with Word 365 it is no longer possible. The only options are Figure and Table, ie. below or above. Who ever heard of such stupidity. I do remember that it involves using a special character (*) but no longer can find it after searching all afternoon. Instead there are "genius" suggestions where we input a table, then parse out the formula and caption. Of course I can do this (I do it for figures all the time) but that is hardly the point. I am afraid we are retro-gressing in our software in that we have more and more workarounds for simple tasks.
I do not recall being able to do what you describe with a simple button click. I've been helping others use Word for more than 25 years.
As you note, if you place your equation in the center cell of a three-column-cell, you can move the caption to the right-most cell after it is created.
Here is my writing on captions: Insert a Caption
From that:
For Equation Captions on the same line, see How to Create Captions for Equations.
Especially for Equations, see: Section 7 Captions and cross-references | Microsoft Word for the Social Sciences
That has been the process as long as I remember. I still have Word 97 and Word 2003 on my computer and that is the method for those.