Media Library widget does not work inside LB

Problem/Motivation

To reproduce:

1. Using 8.7.x
2. Enable Layout Builder and Allow overrides on Basic page
3. Install Media and Media library module
4. Add a Media reference (Image bundle) and use Media library form widget to the Basic block type
5. Create a new node
6. Try to add/edit a custom block and upload a media
7. Media Library widget does not work (should open Media Library popup)

Works as expected when editing custom block independently from LB.
Also, the same setup worked in 8.6.x :( regression?
Also, does not work with IEF widget.

Proposed resolution

Fix Ajax subform handling inside block config form?