How to have a placed object within a text box be centered vertically aligned with with text?

When you added the boxinto the line of text, it was, by default, aligned on the text baseline, same as your text; but now the height of the box is now the biggest "character" height, so ID centers the WHOLE line based on that, so what it's doing is correct. It would do the same thing if you changed/added one letter in that line and made it a much larger size.

Your Text Box Options > Baseline Options can change how this is calculated, but what you want is not possible without doing it a different way, like the suggestion from @James Gifford—NitroPress .

I created a text box, centered a word of type, and set the frame's vertical alignment to center.

I then created a little yellow box and anchored it to the front of the text, and then dragged it to a (smart guide) vertical centering with the text.

Result:

Can you review how you created the elements and connected and positioned them? I suspect it's all in the Anchor Object settings, which might be Inline and pushing the text around. Possibly something incorrect in the Text Frame options as well?