Chrome extension, send message from injected code (world 'MAIN') to background - sendmessage

Question

I have a script that injects a js file in each tab via
chrome.scripting.executeScript({, world: 'MAIN'})
I do that as i want to access variables of the loaded pages.
In this injected code i want to send a message to background via
chrome.runtime.sendMessage()
though in the page console i get the error:
Uncaught TypeError: Cannot read properties of undefined (reading 'sendMessage')
manifest.json (shrinked)
{
"manifest_version": 3,
"background": {
"service_worker": "background.js",
"type": "module"
},
"permissions": [
"scripting"
]
}
background.js
chrome.scripting.executeScript({
target: {tabId: tabId},
files: [
'./js/asdf.js'
],
world: 'MAIN'
}).then()
./js/asdf.js
console.log("asdfasdf"); # is printed
chrome.runtime.sendMessage({action: '...'}).then()
As soon as i do not run the script with world 'MAIN' i can access the method 'sendMessage'.
How can i send infos from a script injected into world 'MAIN' to the background? :)

Answer 1

For my scenario the following worked:
content script (world: isolated)
window.addEventListener("load", async function () {
//get state from background
const state = await chrome.runtime.sendMessage({});
....
//send state to page
window.postMessage();
});
//receive response from page
window.addEventListener("message", (event) => {
//send info to background
chrome.runtime.sendMessage();
}, false);
background.js (inject code into page)
chrome.scripting.executeScript({
target: {tabId: tabId},
files: [
'classes.js',
'.main.js',
],
world: 'MAIN',
}).then();
classes.js
//receive info from content script
window.addEventListener("message", (event) => {
//do something based on received state
}, false);
//post something back to content script
window.postMessage();
process:
get state from background by sendMessage in content script
based on state info content script sends postMessage to page
postMessage triggers process in page (injected code)
code does something and sends postMessage to content script
content script had listened for postMessage and forwards info to background by sendMessage