Instead of Optimization Detective hackily opening its own output buffer via od_buffer_output() during the template_include filter:

In WordPress 6.9 we can now leverage the template enhancement output buffer introduced via Core-43258 (see r60936). When the wp_start_template_enhancement_output_buffer() function exists, we can skip starting our own output buffer:

if ( ! function_exists( 'wp_start_template_enhancement_output_buffer' ) ) {
    add_filter( 'template_include', 'od_buffer_output', PHP_INT_MAX );
}

And then od_template_output_buffer() can be updated accordingly:

if ( function_exists( 'wp_start_template_enhancement_output_buffer' ) ) {
    add_filter( 'wp_template_enhancement_output_buffer', $callback );
} else {
    add_filter( 'od_template_output_buffer', $callback );
}