Sweet alert daha oluşmadan içeride ki objeye erişmeye çalışıyorsunuz bu sebeple addEventListener'dan hata alıyorsunuz.

kodu aşağıda ki gibi güncelleyip tekrar deneyiniz;

<!DOCTYPE html>
<html>
  <head>
    <script src="https://cdn.jsdelivr.net/npm/sweetalert2@10"></script>
    <script>
      function showModal() {
        Swal.fire({
          title: 'Select Options',
          html: `
            <select id="first-select">
              <option value="">Select an option</option>
              <option value="option1">Option 1</option>
              <option value="option2">Option 2</option>
            </select>
            <br><br>
            <select id="second-select" style="display:none;">
              <option value="">Select an option</option>
              <option value="suboption1">Suboption 1</option>
              <option value="suboption2">Suboption 2</option>
            </select>
          `,
          showCancelButton: true,
          confirmButtonText: 'Submit',
        });

        const firstSelect = document.getElementById("first-select");
      const secondSelect = document.getElementById("second-select");
 
      firstSelect.addEventListener("change", function() {
        if (firstSelect.value === "option2") {
          secondSelect.style.display = "block";
        } else {
          secondSelect.style.display = "none";
        }
      });
      
      }
 
      
    </script>
  </head>
  <body>
    <button onclick="showModal()">Show Modal</button>
  </body>
</html>