変更前

manifest.json

{
    ...
    "manifest_version": 3,
    "permissions": [
		"tabs",
		"scripting"
	],
    ...
}

content.js

chrome.runtime.sendMessage({}, () => {});

background.js

chrome.runtime.onMessage.addListener((message, sender, sendResponse) => {
    getNextTabAction();    
	return true;
});


async function getNextTabAction() {

    const next_tab = ...;
	
    chrome.scripting.executeScript({
        target: {tabId: next_tab},
        function: () => {
            console.log("-_-");
        }
      });
          
	return true;
}

エラーコード

caught (in promise) Error: Cannot access contents of url "「タブのURL~」".
Extension manifest must request permission to access this host.

変更後

manifest.json

{
    ...
    "manifest_version": 3,
    "permissions": [
		"tabs",
		"scripting"
	],
	// 以下を追加するだけ
	"host_permissions": ["http://*/*", "https://*/*"],
    ...
}

これで目標のタブ(今回はnext_tab)のコンソールに「-_-」が追加されると思います。