Post Statuses other than Published

Thanks for the help, here's what I've been working with to try and get it to work based on your post and the examples you listed for dealing with a Relationship between one custom post type, (slug='offer'), to another custom post type, (slug='listing'). I've confirmed that the Relationship ID is 'listing-to-offer-relationship' by going to Meta Box > Relationships > Listing to Offer Relationship and copying it from there.

/**
* Allow Meta Box Relationship to use post statuses besides just Published
*/
add_action( 'mb_relationships_init', function() {
	MB_Relationships_API::register([
		'id'   => 'listing-to-offer-relationship',
		'from' => [
			'object_type' => 'post',
			'post_type'   => 'listing',
			'field'       => [
				'query_args' => [
					'post_status' => array( 'publish', 'draft' )
				],
			],
		],
		'to'   => [
			'object_type' => 'post',
			'post_type'   => 'offer',
			'field'       => [
				'query_args' => [
					'post_status' => array( 'publish', 'draft', 'accepted', 'rejected' )
				],
			],
		],
	]);
});

Nothing I test has been working for me though. When I have an custom post type 'offer' in draft I can see the connected custom post type 'listing' just fine. But when I view the connected 'listing' the connected 'offer' is blank. I've tried to set the 'post_type' in both the from and to arrays to 'post' instead of 'offer' and 'listing' which didn't seem to help. I've also tried to wrap it with your example 'function your_prefix_function_name() {' instead of 'add_action( 'mb_relationships_init', function() {' and that didn't work for me either.

I've also tried to add post statuses through the Meta Box interface under Meta Box > Relationships > Listing to Offer Relationship > From > Field > Query args:

key=post_status value=publish
key=post_status value=draft

key=post_status value='publish'
key=post_status value='draft'

key=post_status value=array('publish','draft')

Along with the other matching To > Field > Query args and that didn't work either.

Can you please share some screenshots of the issue (full screen)?

Here are some screenshots of what I'm seeing when I look at the offer and listing:

offer
https://prnt.sc/Db5Vz3vrv5L3

listing
https://prnt.sc/Db5Vz3vrv5L3

And please notice that the custom field (relationship) shows on the object from get object type, post type, and field settings from object to. That means when you edit a listing post, you will see a meta box with a list of offer posts and some post statuses.

I'm not sure I'm understanding what you mean here - when I view either an offer or listing I can see a dropdown for the other related field.

It looks like I didn't copy the listing link correctly, you can see it here:

listing

https://prnt.sc/kERDRa0AiVmx

I'll also send over the site credentials for you to get in and take a closer look.