I think the data parsed from the post_content should be put into another array instead of stuffed back into $post. So maybe:

$snapshots_data = array();
foreach ( $posts as $post ) {
    $snapshots_data[] = $this->get_post_content( $post );
}

And use $snapshots_data instead of $content.

I have changed that, I kept it as such because I thought we will need mapping of post and data. However, I never used that mapping, but now to add uuid in merge_conflcit i will use it,
Creating another array like

$snapshot_post_data = array();
foreach ( $posts as $post ) {
    $snapshot_post_data[] = array(
        'data' => $this->get_post_content( $post ),
        'uuid' => $post->post_name,
    );
}

Better name than $merge_value would be $merged_snapshot_data.

Nice. Better than using the $wp_version global which I usually use. I'll do this in the future.

Maybe leave the winner in the merge conflict intact?

Maybe merge_conflict should use the source UUID as they key for each value here? Then we'll be able to look up later which snapshot the value came from.

Indentation problem.

These lines aren't right. There could be a translation string that has an apostrophe and this would cause a JS error. I suggest refactoring as follows:

jQuery( function( $ ) {
    var optionText = <?php echo wp_json_encode( __( 'Merge Snapshot', 'customize-snapshots' ) ); ?>;
    $( 'select[name="action"], select[name="action2"]' ).each( function() {
        var option = $( '<option>', {
            text: optionText,
            value: 'merge_snapshot'
        } );
        $( this ).append( option );
    } );
} );

Super clean 👍 🙇