ISBAT see my posts live when the Post Carousel or the Posts Blocks are added to my Homepage Template via Site Editor

### Describe the bug:

ISBAT see my posts on the live site when the Post Carousel Block or the Posts Block are added to my Homepage Template within the [Site Editor](https://wordpress.org/documentation/article/site-editor/)

### To reproduce:

1. Start with a site that has an FSE enabled theme like Twenty Twenty-Three for example and the CoBlocks plugin active.
2. Go to Appearance > Theme > Editor > which drops you into your Home page template
3. Click to add a new block, and search for the Post Carousel (CoBlocks) or the Posts (CoBlocks) and add one of them.
4. Save the page and opened it on the live site

### Expected behavior:
I expect the Post Carousel (CoBlocks) or the Posts (CoBlocks) to display the posts on the site.

### Screenshots:

You can see the block in the DOM when you inspect the page, but they're not actually displaying on the front end:

### Isolating the problem:

- [ x ] This bug happens with no other plugins activated
- [ x ] This bug happens with a default WordPress theme active
- [ x ] This bug happens **without** the Gutenberg plugin active
- [ x ] I can reproduce this bug consistently using the steps above

### WordPress version:

Tested on: 6.2.2

### Gutenberg version: