connect a servise worker to a contect script

In short, I want that when you press my extension button from the context menu, the content script (contect-script) will be added to the web page temporarily. I tried to use sendMessage() but it just didn’t work.

Any help will be appreciated:)

//This is the servise worker (eventPage)

chrome.runtime.onInstalled.addListener(() => {
 chrome.contextMenus.create({
   id: 'select',
   title: 'select',
   type: 'normal',
   contexts: ['all']
 });

})
chrome.contextMenus.onClicked.addListener(function (clickDate) {
 if (clickDate.menuItemId == 'select') {
   //send massege to make content-script start operate
  chrome.runtime.sendMessage('start');

 }
});



-------------------------------------------------------------------------


//lets say that this is the content-script
chrome.runtime.onMessage.addListener(function(response,sender,sendResponse){

if(response == 'start'){

// js code that is inserted into the site
}
});
{
"manifest_version": 3,

"name": "SendFast",
"description": "This extension makes it easier to send information",
"version": "1.0",
"icons": {
  "128": "16-nahum.png",
  "48": "64-nahum.png",
  "16": "16-nahum.png"
},

"action": {
  "default_icon": "16-nahum.png",
  "default_popup": "popup.html"
},
"permissions":["contextMenus","activeTab"],


"background":{
  "service_worker": "eventPage.js"
},
"content_scripts": [
  {
    "matches": ["<all_urls>"],
    "js": ["content-script.js"]
  }
]

}