There are plenty of issues open on the subject, but I couldn't find an explanation in my case. Here is a minimal test case:

Here is my manifest.json

{
  "manifest_version": 3,
  "name": "Test",
  "version": "1.0",
  "description": "Test extension",
  "icons": {
    "48": "dark.png"
  },
  "background": {
    "service_worker": "button.js"
  },
  "permissions": [
    "activeTab"
  ],
  "action": {
    "default_icon": "dark.png",
    "default_title": "DarkTheme"
  },
  "content_scripts": [
    {
      "matches": [
        "<all_urls>"
      ],
      "js": [
        "dark.js"
      ]
    }
  ]
}

button.js

chrome.action.onClicked.addListener(tab => {
  console.log('clicked')
  chrome.tabs.sendMessage(tab.id, { value: false })
});

dark.js

chrome.runtime.onMessage.addListener(request => {
  console.log('received', request)
})

So, basically, my listener is set right at the start, and only when I press the button do I send a message. How come I can receive this error when I press the button?

Uncaught (in promise) Error: Could not establish connection. Receiving end does not exist.

Tested on Chromium Version 100.0.4896.75 (Build officiel) snap (64 bits)