I thought I would follow up with one final post about this in case anyone in the future needs help resolving it. Because of the impact the issue was having, I decided to dive in and work out my own fix. I have essentially changed the theme files I was using (boost theme) to update the embedded layout rule to point to different versions of embedded.php and embedded.mustache which add in the blocks column. I've carefully documented this process and included some sample files for an older and newer version of moodle. See attached zip file.
In the long term I would see the best fix in core to be either my fix, although I don't know all the contexts in which embedded layout is used and therefore cannot comment on undesirable side effects. OR an additional layout is created for LTI
specific embedded based on my fix.
I checked the impact of not
having the blocks show against a range of tools. Quizzes are serious impacted. The Book resource tool will not show the Chapter block. I was unable to test the Workshop tool due to the amount of effort required to set it up. All other tools/resources did not have any dependencies on the side blocks and therefore aren't impacted by this issue.
I've also updated my bug report with the attached with the hope that a fix makes its way into the core code in the future.
Thanks to Daniel for giving me the initial pointer in the code so I could start to unpick the problem.
Fix for LTI embedded layout issue.zip