How to backup my WordPress hosted blog

I have no actual experience with what you are concerned about, but I did find this partway down a page:

When you transfer using the import file, all attached images are downloaded and the link is updated.
https://www.wpbeginner.com/wp-tutorials/how-to-properly-move-your-blog-from-wordpress-com-to-wordpress-org/

Here is what your new host says:
https://support.hostgator.com/articles/specialized-help/technical/wordpress/transfer-wordpress-from-wordpress-com-to-your-self-hosted-wordpress

Then, you also have this option:

The Guided Transfer is a one-time fee of $129.00 per blog transferred, and is available for purchase in your dashboard in Tools -> Export.

(Note: If you don’t see the Guided Transfer option on that page, you likely have a Premium Theme or use Custom Fonts, which do not transfer. If you use a Premium Theme, you’ll need to switch your site to a free theme. If you use Custom Fonts, you’ll need to switch back to your theme’s default fonts. Once you do, you can add the Guided Transfer upgrade to your shopping cart.)
https://en.support.wordpress.com/guided-transfer/

Please make sure you’re posting on the WordPress.COM forums: https://en.forums.wordpress.com/