Infinite Scroll: 'Load more posts in page with a button' doesn't work in Twenty Twelve theme

### Impacted plugin

Jetpack

### Quick summary

Infinite Scroll documentation (https://jetpack.com/support/infinite-scroll/) shows how to use 'Load more posts in page with a button' in the Twenty Twelve theme. It doesn't work, and the site behaves like the 'Load more posts as the reader scrolls down' option was active.

It would also make sense to clarify the button name as the documentation mentions 'Load more posts', but the code says 'Older posts'.

### Steps to reproduce

1. Enable the Twenty Twelve theme for a site and add a few posts
2. Navigate to Jetpack -> Settings -> Writing and enable 'Load more posts in page with a button' option
3. Open the post list

### A clear and concise description of what you expected to happen.

The "Older posts" button is displayed.

### What actually happened

The button is not displayed, and posts are loaded on scroll.

### Impact

Some (< 50%)

### Available workarounds?

No but the platform is still usable

### Platform (Simple and/or Atomic)

_No response_

### Logs or notes

_No response_

Start with the Jetpack Infinite Scroll documentation and reproduce the issue through Jetpack → Settings → Writing using the Twenty Twelve theme and a post list. Verify why the “Older posts” button is absent and scrolling loads posts instead; done means the button appears for the button option and the documentation uses the matching name.

Written by the indexing model from the issue text.