Yup, exactly. The idea of the space on either side being “nothing” is extremely hard to fathom for me honestly, but it’s the only way to interpret an expanding finite universe (that I know of).

No, you’re misunderstanding my analogy. In the balloon example, the surface of the balloon is the universe. The center of expansion is nowhere in the universe in that analogy. Another way to say it would be: can you point to the location in the universe which is the center of expansion? Can you go there (if you could teleport)? The answer to both questions is no.

Also I’m not sure what you were saying about an infinite universe so perhaps we agree, but there certainly is not a center to an expanding infinite plane.

No, that is incorrect. Imagine if the earth was expanding like a balloon. Which point on the surface of the earth would be the “center” of expansion? None would be, the universe is hypothesized to be similar