Change background color on format-image posts

That’s indeed possible, but you will not be able to use the colorposts_css_output filter to do that. You will need to hook somewhere else to inject that CSS. Here is an example below, where I build the CSS and inject it to the head of the page. You’ll note that the CSS I target is specific to my theme; you’ll need to adapt it to yours:

<?php
/**
 * Posts Colors plugin extension.
 * Build CSS to be inserted in the head of the page.
 * 
 * URL: https://projectdmc.org/support/topic/change-background-color-on-format-image-posts/
 *
 * This is a generic implementation,
 * but your theme may come with better hooks
 * that come right before the post loop on the home page,
 * or at the top of a single post in a post grid.
 * I would recommend using your theme's hooks when possible.
 *
 * @return void
 */
function jeherve_post_colors_aeriksson() {
	// Do not add any CSS to RSS feeds or embeds.
	if ( is_feed() || is_embed() ) {
		return;
	}

	// Only proceed if we're on the blog home page.
	if ( ! is_home() ) {
		return;
	}

	// Build an array of Post IDs for the posts displayed on the home page.
	global $posts;
	if ( empty( $posts ) ) {
		return;
	}

	$post_ids = wp_list_pluck( $posts, 'ID' );

	// The $post_css variable will store our CSS.
	$post_css="";
	foreach ( $post_ids as $post_id ) {
		// Fetch colors for this post.
		$post_colors = get_post_meta( $post_id, '_post_colors', true );
		
		// If no colors are stored for this post, bail.
		if ( empty( $post_colors ) ) {
			continue;
		}
		
		// Fetch the 2 colors stored for that post.
		$color    = $post_colors['color'] ?? ''; // this is an hexadecimal color code without #, e.g. '33f078'.
		$contrast = $post_colors['contrast'] ?? ''; // This is an RGB value for a color, e.g. '51, 240, 120'.
		
		// If for some reason no colors were saved, bail.
		if ( empty( $color) || empty( $contrast ) ) {
			continue;
		}

		/*
		* Build our CSS, and append it to the existing $post_css variable.
		* This will be highly dependent on your theme's markup.
		*/
		$post_css .= sprintf(
			'
			.content-area article#post-%1$d h2.entry-title a {
				background-color: #%2$s;
				color: rgb(%3$s);
			},
			.content-area article#post-%1$d h2.entry-title a:hover {
				color: rbga(%3$s, 0.8);
			}
			',
			esc_attr( $post_id ),
			esc_attr( $color ),
			esc_attr( $contrast )
		);
	} // End our loop through the posts.

	// Finally, inject our CSS.
	if ( ! empty( $post_css ) ) {
		printf(
			'<!-- Generated by a Post Colors extension -->%1$s<style type="text/css">%2$s</style>',
			PHP_EOL,
			$post_css
		);
	}
}
add_action( 'wp_head', 'jeherve_post_colors_aeriksson' );