Content security policy blocking injecting styles into pages

I am working on an extension that will inject some elements into the webpages using content scripts.

i used react/webpack to build the extension. but when i am trying to use the extension, in some websites like secure.login.gov the styles are not getting injected. i am getting the following error in console.

Content-Security-Policy: The page’s settings blocked an inline style (style-src-elem) from being applied because it violates the following directive: “style-src ‘self’ https://secure.login.gov ‘nonce-83e27ef5530a894f4f0ee9c5323940ea’

there is no issue in chrome/edge where i am using manifest v3 where as in firefox i am using manifest v2.

i tried instructions in here https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/WebExtensions/manifest.json/content_security_policy. but this looks like will be applied to extension pages not the actual web pages

any help on this will be appreciated.