Can I set up a type-search-and-select choice question in Qualtrics?

You can do this, if you use a bit of CSS and JavaScript. Just copy the below code in to the HTML part of a text question. Once you see how it works, you can modify to use data from Qualtrics and to add the result in a Qualtrics question.

Here is the Example:

Find fruit:
  <style>
    body {
      font-family: Arial, sans-serif;
      display: flex;
      justify-content: center;
      align-items: center;
      height: 100vh;
      margin: 0;
    }
    #search-input {
      padding: 10px;
      font-size: 16px;
    }
    #result-list {
      list-style: none;
      padding: 0;
      margin: 0;
      position: absolute;
      background-color: #f9f9f9;
      box-shadow: 0 2px 4px rgba(0, 0, 0, 0.1);
      display: none;
    }
    #result-list li {
      padding: 10px;
      cursor: pointer;
    }
    #result-list li:hover {
      background-color: #ddd;
    }
  </style>
  <input type="text" id="search-input" placeholder="Type to search...">
  <ul id="result-list"></ul>

  <script>
    // Sample array for demonstration
    const dataArray = ['Apple', 'Banana', 'Cherry', 'Date', 'Grape', 'Lemon', 'Orange', 'Peach', 'Pear', 'Plum'];

    const searchInput = document.getElementById('search-input');
    const resultList = document.getElementById('result-list');

    // Event listener for input field
    searchInput.addEventListener('input', function() {
      const inputValue = searchInput.value.toLowerCase();
      const filteredArray = dataArray.filter(item => item.toLowerCase().includes(inputValue));

      // Display filtered results in the dropdown
      displayResults(filteredArray);
    });

    // Function to display search results in the dropdown
    function displayResults(results) {
      // Clear previous results
      resultList.innerHTML = '';

      // Display results in the dropdown
      results.forEach(result => {
        const listItem = document.createElement('li');
        listItem.textContent = result;
        listItem.addEventListener('click', function() {
          // Set selected result in the input field
          searchInput.value = result;
          // Clear the dropdown
          resultList.innerHTML = '';
        });
        resultList.appendChild(listItem);
      });

      // Show the dropdown
      resultList.style.display = results.length > 0 ? 'block' : 'none';
    }

    // Close the dropdown if the user clicks outside of it
    window.addEventListener('click', function(event) {
      if (!event.target.matches('#search-input')) {
        resultList.style.display = 'none';
      }
    });
  </script>

Thank you so much. I copied your code here, but it didn’t work. Did I do the right thing, or I need to copy your code elsewhere?

Thanks! Very helpful!

I’m guessing you changed it to Simple layout. If so, you’ll need to load jQuery. You can only use select2 on multiple choice select boxes because dropdowns aren’t select elements in Simple layout. You also can’t use it on side-by-side or drill-down questions for the same reason. 

With Flat theme you should not load jQuery - it is already loaded. You may need to adjust your jQuery selector(s) as the DOM is quite different than Simple layout.