Hi Casper,
Thanks a lot for your kind reply. I can understand this issue better now.
Firstly, I was wondering did you concern about the tool list at the new email page bottom as the following screenshot shows: 
If yes, I have checked two testing tenant and found that one of the demo accounts has this tool list at the bottom and another one does not have it. As I mentioned before, I searched on this issue and found that there are many people who are facing this issue now.
I found that seems that the Product group are doing some updating on the OWA UI and want to move the tool list options to the top side, so some users will not be able to see this now.
I found a thread which mentions that the issue might be caused by the org releasing settings, if you are set to be targeted releasing user, you will be missing the tool list in the bottom and the options will appear on the top side. This can work for one of my workmate's tenants, so I'd like to share this thread to you then you can have a try.
How to move the send button to the bottom? - Microsoft Community
Then I used my demo account which does not have the tool list at the bottom to add the add-ins according to your reply. I noticed that in the settings, it mentions the "actions and add-ins you want to see when you select a message to read". It does not show in the bottom of new emails, but I can see it when I read emails in my inbox. I think it's a design limitation for this Message surface feature.


Then I tried to new an email and when I click the "..."at the top side tool list, I can see the add-ins which I added into the Message surface, I was wondering whether you can see that from your side? if yes, you can insert add-ins using this option.

As I mentioned before, this issue might be caused by the product releasing and need to be resolve from the back end, if the issue still persists and no work around work is available at your side, I suggest you submit a service request according to the steps I shared in my first reply, this is the most efficient way to get the support from the professional engineers who have the permission to check at the back end.
Appreciate your patience and understanding and thank you for your time and cooperation. Please feel free to let me know if there is any feedback from your side.
Sincerely,
Sherry | Microsoft Community Moderator