With wordpress 6.6, and Gutenberg 19, you can activate an experiment for "UI to create block bindings".
Block Bidings are available from WP 6.5, but in core, without user interface.
Custom fields defined with Meta Box are not available for selection.
I'm a new user of Meta Box, and hoped that this could mean this would work out of the box:
"Meta Box saves each field in a single line in the database, corresponding to a meta_key - meta_value and it's compatible with the way WordPress interacts with custom fields through the get_post_meta or update_post_meta."
Best regards, Oscar