Sharing buttons: Discrepancies between themes on homepage / archive pages

### Impacted plugin

Jetpack

### Steps to Reproduce

Adding this issue as a 'main' issue of sorts, to collect examples of discrepancies between themes in terms of sharing / like button visibility, specifically in relation to home / archive pages.

To replicate the issue, activate one of the following themes: Twenty Twenty Two, Catch FSE, OceanWP, Blockbase, Pistache.

1. On a Jetpack connected site, make sure sharing and / or like buttons are enabled from Jetpack > Settings > Sharing.
2. From Settings > Sharing, make sure 'Front Page, Archive Pages and Search Results is checked.
3. From Settings > Reading, make sure that the home page is set to display latest posts.
4. Those mentioned themes don't show sharing buttons underneath posts on the homepage / archive pages (and did not in prior versions of Jetpack either).

The Twenty Twenty Two theme behavior was observed in[ this issue comment](https://github.com/Automattic/jetpack/pull/24896#issuecomment-1171189768), and in internal testing here: p8oabR-Uj-p2#comment-6511

As an aside, I've also checked for discrepancies between Jetpack versions on different themes. Nothing found as yet (where an older Jetpack version includes sharing buttons under posts on the homepage and the beta version doesn't, and vice versa).

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

Where possible, consistency between themes in terms of sharing button behavior.

### What actually happened

As above - inconsistency in some cases.

### Browser

Google Chrome/Chromium

### Other information

_No response_

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

Self-hosted

### Reproducibility

Consistent

### Severity

_No response_

### Available workarounds?

_No response_

### Workaround details

_No response_

Reproduce the behavior on a Jetpack-connected self-hosted site using Twenty Twenty Two, Catch FSE, OceanWP, Blockbase, and Pistache, with sharing enabled for the front page, archive pages, and search results. Compare the homepage and archive-page output across themes, starting with the behavior documented in the linked pull-request comment; done means the relevant sharing-button behavior is consistent where supported.

Written by the indexing model from the issue text.