Custom block types(non reusable) is not pulled if used in Layout Builder

Problem summary

I'm using Entity share module to deploy content from one environment(staging) to another (production). I’m able to deploy custom content types and custom block types. But When I try to deploy a custom content type that is using Layout Builder and added custom block types directly in Layout builder.

Steps to reproduce

Setup two vanilla Drupal instances for server(server.ddev.site) and client (client.ddev.site).
Activity on Server application :

1. Enable Layout builder module and apply for Article content type for manage display. Add new article page via Layout builder and add a Custom block (Basic block) direct on Layout builder.
2. Create a channel for Article content and add required configuration.

Activity on Client application

1. Try to pull the Article contents from server.
2. Articles will be imported but Custom blocks is not going to import.

NOTE : Content type and their field related configuration should be same on both the environments.

Proposed-resolution

Custom block type (non-reusable) should be pulled the same as other custom block types (reusable which is shown in the Custom block library)