You can use the get HTTP method to send the id of the song to the details.php page and query to the database on that id.

And it's always a good practice to use the GET HTTP method for searching actions. As mickmackusa said in the comment:

$_POST is most appropriate when "writing" data server-side. $_GET is most appropriate when "reading" data server-side.

So change the code on the Home page as below:

<?php
require_once '../config.php';
// query changed to fetch id as well
$sql = 'SELECT id , title FROM song ORDER BY title ASC;';
$stmt = $conn->prepare($sql);
$stmt->execute(['title' => $title]);
// fetch all rows
$songTitle = $stmt->fetchAll(PDO::FETCH_ASSOC);
?>


<!-- here we change the method to get -->
<form action="chord/details.php" method="get" class="p-3">
  <div class="input-group">
            <input type="text" name="search" id="search" class="form-control form-control-lg rounded-0 border-primary width =250px;" placeholder="Search..." autocomplete="off" required>
            <div class="input-group-append">
              <input type="submit" name="submit" value="Search" class="btn btn-primary rounded-right">
            </div>
   </div>
</form>


<?php 
    foreach ($songTitle as $song) {
        // we add the id to the link
        echo "<a href='chord/details.php?id={$song['id']}'>{$song['title']} <br> </a>";
    } 
?>

And change the detail.php like below:

<?PHP
//This is working fine with Search Bar
require_once '../config.php';

if (isset($_GET['search']) OR isset($_GET['id'])) {

    $condition = "";
    $value = "";
    if (!empty($_GET['id'])) {
        $condition = "id = :value";
        $value = $_GET['id'];
    }
    elseif (!empty($_GET['search'])) {
        $condition = "title = :value";
        $value = $_GET['search'];
    }

    $sql = 'SELECT * FROM song WHERE ' . $condition;
    $stmt = $conn->prepare($sql);
    $stmt->execute(['value' => $value]);
    $row = $stmt->fetch();


} else {
    header('location: .');
    exit();
}

?>

//Display the song lyrics here
<div>Original Key: <?= ucfirst($row['chord']) ?></div><br>
<pre data-key=<?= ucfirst($row['chord']) ?> id="pre">
              <?= ucfirst($row['lyrics']) ?>
</pre>

It's also a good idea to use LIKE for searching in the title like below:

if (!empty($_POST['search'])) {
    $condition = "title LIKE :value";
    $value = "%" . $_POST['search'] . "%";
}

Assuming you have an id column in the song table. You could do something like this:

<?php
require_once '../config.php';
$sql = 'SELECT id, title FROM song ORDER BY title ASC;';
$stmt = $conn->prepare($sql);
$stmt->execute();
// fetch all rows
$songTitle = $stmt->fetchAll(PDO::FETCH_ASSOC);
?>


//Search bar

<form action="chord/details.php" method="post" class="p-3">
  <div class="input-group">
            <input type="text" name="search" id="search" class="form-control form-control-lg rounded-0 border-primary width =250px;" placeholder="Search..." autocomplete="off" required>
            <div class="input-group-append">
              <input type="submit" name="submit" value="Search" class="btn btn-primary rounded-right">
            </div>
   </div>
</form>



// Here I display all my songs from the database using their title
<?php 
    foreach ($songTitle as $song) {

      // I'm not sure how to modify here.
     echo "<a href='chord/details.php?id=".$song['id]."'>{$song['title']} <br> </a>";
} ?>

Details page

//This is working fine with Search Bar
<?php
require_once '../config.php';
if (isset($_POST['submit'])) {
  $title = $_POST['search'];
  $sql = 'SELECT * FROM song WHERE title = :title';
  $stmt = $conn->prepare($sql);
  $stmt->execute(['title' => $title]);
  $row = $stmt->fetch();

} elseif (!empty($_REQUEST['id'])) {
  $sql = 'SELECT * FROM song WHERE id = :id';
  $stmt = $conn->prepare($sql);
  $stmt->execute(['id' => $_REQUEST['id']]);
  $row = $stmt->fetch();
} else {
  header('location: .');
  exit();
}
?>

//Display the song lyrics here
<div>Original Key: <?= ucfirst($row['chord']) ?></div><br>
<pre data-key=<?= ucfirst($row['chord']) ?> id="pre">
              <?= ucfirst($row['lyrics']) ?>
</pre>