Weird issue after moving wordpress

So, I moved WP to a new domain, everything looks and works well, but there must be some db bug: the media files transferred properly and show the new url in the media library, but the source code of the site shows the old file path (old domain).

Could this plugin solve the issue or should I look for the root cause?

See it here: sunshinemorrobay.com

Thanks!

https://www.ads-software.com/plugins/relative-image-urls/