Normally, I migrate web sites from server to server via SSH. I have migrated dozens of large database sites with mysqldump from the terminal. After that I clear cache and update the "friendly urls" and everything works fine. I do it all the time and it always works for me, I have never used a migration plugin.
However, the story is different with Elementor. When I migrate sites with Elementor, always the menus and some templates with shortocodes do not end up displaying correctly and I have to make some manual adjustments. I know there are migration plugins that migrate without breaking anything. The problem with these plugins, is that they are for small or standard databases.
How can I migrate an Elementor website with mysqldump without breaking anything and without using wordpress plugins?

Technically, there should not be any difference from a regular migration. For all intents and purposes, a shortcode is just text. How do they break exactly?