There is no conditional tag for the blog page. You have to use both is_home() and is_front_page() to detect this page
When you use is_home() and is_front_page(), you have to use them in the right order to avoid bugs and to test every user configuration:
<?php
if ( is_front_page() && is_home() ) {
// blog listings
} elseif ( is_front_page() ) {
// static homepage
} elseif ( is_home() ) {
// blog page
} else {
//everything else
}
?>
Taken from https://codex.wordpress.org/Conditional_Tags
If you want to check it another way, the posts / frontpage is stored in the database as an option which we can get the data using get_option which we can use:
get_option('show_on_front');
We can then do a check on that like so:
$front_page_type = get_option('show_on_front');
if($front_page_type="posts") {
// blog page
} else {
// static front page
}