I don't recall if I've encountered that specific problem in tampermonkey (or if I did and it didn't cause a problem worth remembering), but you can run things in the extension's context as well to bypass certain restrictions, as well as use special extension provided functions (GM_* from the greasemoney standard) that allow for additional actions.
I do recall intercepting requests when I used a chrome extension to change CSP values though and not needing to when doing something similar later in tampermonkey, but it may not have been quite the same issue as you're describing, so I can't definitively say whether I had a problem with it or not.
I do recall intercepting requests when I used a chrome extension to change CSP values though and not needing to when doing something similar later in tampermonkey, but it may not have been quite the same issue as you're describing, so I can't definitively say whether I had a problem with it or not.