Can not import JQuery to a chrome extension

I'm trying to add the following function to a chrome extension:

$( function() {
    var availableTags = [
      "ActionScript",
      "JavaScript",
      "Lisp",
      "Perl",
      "PHP",
      "Python",
      "Ruby",
      "Scala",
      "Scheme"
    ];
    $( "#other" ).autocomplete( {
      source: availableTags,
      minLength: 0
    })
    .focus(function() {
        $(this).autocomplete('search', $(this).val())
    })
    ;
  } );

But I kept getting the error:

counterstring.js:7 Uncaught (in promise) ReferenceError: $ is not defined
    at show_options (VM182 counterstring.js:7)
    at VM182 counterstring.js:81
    at Array.forEach (<anonymous>)
    at VM182 counterstring.js:78

EDIT:

I have updated the manifest file as suggested in the comments, but still getting errors. This is the current version I have:

    "content_scripts": [ {
      "matches": ["http://*/*", "https://*/*"],
      "js": ["js/jquery-3.5.1.min.js", "js/jquery-ui.min.js", "js/counterstring.js"]
  }],
    "background": {
        "persistent": true,
        "scripts": ["js/jquery-3.5.1.min.js","js/jquery-ui.min.js","js/background.js","js/counterstring.js"]
      },
    "permissions": [
         "contextMenus",
         "activeTab", 
         "storage"
       ],

Now I'm only imported jquery 3.5xxx and also jquery-ui since I read it is also required for the autocomplete function.

From this I'm still getting the same error:

Uncaught (in promise) ReferenceError: $ is not defined
    at show_options (VM238 counterstring.js:6)
    at VM238 counterstring.js:80
    at Array.forEach (<anonymous>)
    at VM238 counterstring.js:77

Also, if I tried without importing jquery-ui I get this other error:

Uncaught (in promise) TypeError: $(...).autocomplete is not a function
    at show_options (VM274 counterstring.js:6)
    at VM274 counterstring.js:80
    at Array.forEach (<anonymous>)
    at VM274 counterstring.js:77

Which I interpret is it is importing jquery with that code, but still not finding the function I need.