After attaching block_content entities to a block the only place that shows an integration between the the block and the block_content entities is in the contextual menu. If that is disabled, there is no way to easily see that relationship. Especially if the parent block's title has been changed.
Once a block_content entity exists, there is no easy way from the block_content entity to connect it to a block. This can only be done during the content_block creation.
Create block_content, go to the block layout, find and edit the parent block. There is no link on the block form that shows the block_content entity.
Edit a block_content entity. On that form, there is no way to link it to a block or a link to existing block entities.
block entity should have links to edit any associated content relationship.
block should have an option to change or repair the block_content relationship. block_content entity should have links to the edit form for every parent block entity and an option to connect to a new block as it does on creation. I have attempted to build hooks or plugins to accomplish this, but it seems like it is a more complicated process than it seemed at first.
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10.3 ✨
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If there is any reason why one needs multiple ways to access related content, let my obsessive minor re-edits of my original post serve as an example.
Changes are made on on 11.x (our main development branch) first, and are then back ported as needed according to our policies.