How to add space between two buttons?

In my homepage header, I have a login and register button. Currently, there is no space between these two buttons in wide screen. In smaller screen, I made it to collapse, and there is space.

How do I keep the space regardless of the screen size?

I've tried to add mb-2 in the li and ul tags, but it only works when they collapse.

<!DOCTYPE html>
<html lang="en">

<head>
  <meta charset="utf-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1" />
  <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.3.3/dist/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-QWTKZyjpPEjISv5WaRU9OFeRpok6YctnYmDr5pNlyT2bRjXh0JMhjY6hW+ALEwIH" crossorigin="anonymous">
  <script src="https://cdn.jsdelivr.net/npm/bootstrap@5.3.3/dist/js/bootstrap.bundle.min.js" integrity="sha384-YvpcrYf0tY3lHB60NNkmXc5s9fDVZLESaAA55NDzOxhy9GkcIdslK1eN7N6jIeHz" crossorigin="anonymous"></script>
</head>

<body>
  <header>
    <nav class="navbar navbar-expand-lg navbar-light bg-light">
      <div class="container">
        <a href="home" class="navbar-brand">
          <img class="img-responsive" src="/image/logo.png" alt="Logo" />
        </a>
        <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarSupportedContent" aria-controls="navbarSupportedContent" aria-expanded="false" aria-label="Toggle navigation">
            <span class="navbar-toggler-icon"></span>
          </button>
        <div class="collapse navbar-collapse" id="navbarSupportedContent">
          <ul class="navbar-nav me-auto mb-2 mb-lg-0">
            <li class="nav-item mb-2">
              <button type="button" class="btn btn-outline-primary btn-sm" mr-1 href="#">
                  Register
                </button>
            </li>
            <li class="nav-item mb-2">
              <button type="button" class="btn btn-primary btn-sm" href="#">
                  Log in
                </button>
            </li>
          </ul>
          <form class="d-flex">
            <input class="form-control me-2" type="search" placeholder="Search" aria-label="Search" />
          </form>
        </div>
      </div>
    </nav>
  </header>
</body>

</html>

Solution

The navbar in Bootstrap uses Flexbox. The direction is controlled through flex-direction.
Having that in mind you could know, that you should not add margin to space the list items apart. Instead, use the gap property on the list container.

remove mb-2 from the <li>
add gap-2 to the <ul>

<!DOCTYPE html>
<html lang="en">

<head>
  <meta charset="utf-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1" />
  <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.3.3/dist/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-QWTKZyjpPEjISv5WaRU9OFeRpok6YctnYmDr5pNlyT2bRjXh0JMhjY6hW+ALEwIH" crossorigin="anonymous">
  <script src="https://cdn.jsdelivr.net/npm/bootstrap@5.3.3/dist/js/bootstrap.bundle.min.js" integrity="sha384-YvpcrYf0tY3lHB60NNkmXc5s9fDVZLESaAA55NDzOxhy9GkcIdslK1eN7N6jIeHz" crossorigin="anonymous"></script>
</head>

<body>
  <header>
    <nav class="navbar navbar-expand-lg navbar-light bg-light">
      <div class="container">
        <a href="home" class="navbar-brand">
          <img class="img-responsive" src="/image/logo.png" alt="Logo" />
        </a>
        <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarSupportedContent" aria-controls="navbarSupportedContent" aria-expanded="false" aria-label="Toggle navigation">
            <span class="navbar-toggler-icon"></span>
          </button>
        <div class="collapse navbar-collapse" id="navbarSupportedContent">
          <ul class="navbar-nav me-auto mb-2 mb-lg-0 gap-2">
            <li class="nav-item">
              <button type="button" class="btn btn-outline-primary btn-sm" href="#">
                  Register
                </button>
            </li>
            <li class="nav-item">
              <button type="button" class="btn btn-primary btn-sm" href="#">
                  Log in
                </button>
            </li>
          </ul>
          <form class="d-flex">
            <input class="form-control me-2" type="search" placeholder="Search" aria-label="Search" />
          </form>
        </div>
      </div>
    </nav>
  </header>
</body>

</html>