Rebalance theme: Sharing buttons are not displayed on the Front Page (wpcom simple)

### Quick summary

Sharing buttons are not displayed on the front page despite enabling the `Front Page, Archive Pages, and Search Results` option for the `Show like and sharing buttons on` setting as in this screenshot:

### Steps to reproduce

1. From https://wordpress.com/marketing/sharing-buttons enable the `Front Page, Archive Pages, and Search Results` checkbox for the `Show like and sharing buttons on` option.
2. Click the "Save Changes" button.

### What you expected to happen

Sharing and Like buttons are displayed on the front (Posts page) page of the site.

### What actually happened

Sharing and Like buttons are not displayed on the front page (Posts page).

### Context

5463340-zen

### Platform (Simple, Atomic, or both?)

Simple

### Theme-specific issue?

Rebalance

### Browser, operating system and other notes

_No response_

### Reproducibility

_No response_

### Severity

_No response_

### Available workarounds?

_No response_

### Workaround details

_No response_

Start by reproducing the issue on a WordPress.com Simple site using the Rebalance theme, with the “Front Page, Archive Pages, and Search Results” setting enabled. Trace where sharing and Like buttons are rendered for the front (Posts page); done means both buttons appear there after saving the setting.

Written by the indexing model from the issue text.