Hi,
This issue has gone 30 days without any activity. This means it is time for a check-in to make sure it is still relevant. If you are still experiencing this issue with the latest versions, you can help the project by responding to confirm the problem and by providing any updated reproduction steps.
Thanks for helping out.

I can reproduce this issue. It's caused by the align wrapper that classic themes use in the editor to wrap blocks with alignment. This means that the element that's receiving the text-align: center style used to center align the block is a div with a block type display, instead of an img with an inline type. text-align: center doesn't work with block display.

If the align wrappers need to be maintained for back compat, then it might be worth considering using flex styles for the center align instead.

It seems to need both text-align: center on the block and margin: 0 auto for the inner element.

Maybe avatar/editor.scss could have something like this:

.wp-block[data-align="center"] > .wp-block-avatar,
.wp-block-avatar.aligncenter  {
	text-align: center;

	& .components-resizable-box__container {
		margin: 0 auto;
	}
}