The following doesn't answer the question, but, rather, might provide some reasoning that makes the idea of such permissions un-desired with a stock moodle.
Themes in moodle are inline ... meaning a change to a theme could affect all users ... regardless of their role and whatever level. Besides, if there were such permissions, don't think those could be restricted to just inserting an image and stuff that would do no damage to the rendering (like css etc.)
That's in a stock moodle ... however, there are forks of Moodle called Totora or Iomad which might provide what you seek.
Have had experience with troubleshooting moodles that had multiple admins more than once where one of the admins thought they were affecting only a category theme and it was really the site default. One recent 'job' to upgrade a moodle from 2.6.x to highest ended with an issue of disappearance of course admin menu .... without that, no way to edit a course. I suspect it was done to the site custom theme not at the front page level, but at category/course level ... just happened to affect the entire site.
Both of those wreaked havoc on the entire site .... affected all users ... all courses, etc.. (inline themes)
My two cents, of course.
Might be wrong also ... the experts in the themes forum might have some thoughts/methods. While posting the same issue in two forums is generally frowned upon, you might post something similar in the themes forum.
'spirit of sharing', Ken