I will give this a try, will let you know. I did notice, it’s not just the header button, but also the AI composer helper that has the same issue.
UPDATE
I found the bug for you, it has to do with group privacy.
Every value below this (owners/owners+mods) will result into hiding the button. Not sure if this is documented somewhere, might have missed it.
Adding the bot to the group, did not make any difference. Changing the above shown visibility setting did.