Recently, in MV3, google supposedly outlawed running remote code in extensions. 
While it may be unsafe, there's also valid business reasons for wanting to.

Here's a few steps on how to do it currently, as of 2023-04-19.
1. Create a sandbox html page, for executing arbitrary code.
2. create a tab that acts as an intermediary between bgsw and the sandbox. Embed the iframe of sandbox in the tab.
3. create a background service worker (bgsw) such that it creates the tab as an offscreen document. ( https://developer.chrome.com/docs/extensions/reference/offscreen/ 

Then, to run the code in the background.
1. send chrome.runtime.message to tab
2. tab then does a iframe.contentWindow.postMessage to sandbox
3. sandbox evaluates the code, then does a window.postMessage back to tab
4. tab takes the info and does a chrome.runtime.message back to bgsw