try to implement this css class :

.no-scrollbar::-webkit-scrollbar {
    display: none;
  }

The best way to fix overflow in mobile devices is through responsive design.

Use a media query for mobile devices, and then inside of it, fix the part overflowing.

It would look like

@media only screen and (max-width:760px){
   //adjust padding
}

And make sure you have this inside your html head tags in your html file

<meta name="viewport" content="width=device-width, initial-scale=1">

When I am viewing my page with these settings on my desktop, the website seems to have no problem.
But when I open my page on my mobile device, the navigation bar overflows and makes the page horizontally scrollable.

How I want my page to work?
I want the page to be horizontally non-scrollable, and make the navigation bar elements centered and adapt with the resolution of my device. However, I don’t want the navigation bar to expand beyond 650px. I have set the header background to red for showing the overflow I get on my mobile device.

header *{
  margin-bottom: 0px;
  padding-left: 3.5vw;
  padding-right: 3.5vw;
  padding-top: 10px;
  margin-top: 0px;
  margin-left: auto;
  margin-right: auto;
  margin-bottom: 0px;;
  max-width: 650px;
  background-color: red;
  color: #cacaca;
  text-decoration: none;
  display: flex;
  justify-content: space-between;
  align-items: center;
  flex-wrap: nowrap;
}

.nav_links {
  list-style: none;
}

.nav_links li {
  display: inline-block;
  padding: 0px 0px;
}

.nav_links li a {
  transition: all 0.3s ease 0s;
}

.nav_links li a:hover {
  color: #ffffff;
  transition: all 0.3s ease 0s;
}