Is there a way to use the eyedropper tool while typing?
I cant' type "I" to select it, because that just inserts the letter i.
TLDR: alt-eyedropper applies the copied style like a paintbrush
This answer is actually easier than what you're asking for -- you don't have to navigate to get to the next text you want to format.
Suppose that you want to use the eyedropper to modify parts of a text block but not the whole block. For example, to change the font on a bunch of different header lines or to change a bunch of words to italic.
You can’t activate the eyedropper while you’re editing, but you can get the same utility using the option key, applying it to specific words or phrases, while skipping around the document.
You don’t have to navigate to get to the text you want to format.
Using the option key:
Note: It's frustrating that the text selection is invisible, but text formatting is updated as desired.
ESC key then the i key.
Because the Eyedropper Tool has no function when editing text, you have to exit the text editing mode first. The ESC will do that.
If the intent is to use the Eyedropper Tool while still in text editing mode, I don't think that's possible. Any tool switch results in leaving text editing mode.