How do I migrate meta boxes from the Classic Editor to the “side area” in Gutenberg Editor?

The area is called the same. Just side, for sidebar.

I found help for migration here: https://wordpress.org/gutenberg/handbook/extensibility/meta-box/

The PHP, for setting up your meta field to migrate, code needs some tweaks. First set in following as new argument on your meta field setup

array(
    '__block_editor_compatible_meta_box' => false,
)

let’s you decide on next load of the backend, if you want to use the old or gutenberg editor.

and then you shall insert this, which kind of finishes the migration:

array(
        '__back_compat_meta_box' => false,
    )