Form being submitted despite an existing php code meant to validate it

Question

I'm trying to validate a form i have on the serverside using php, the code of the php itself doesn't show errors, but the form gets submitted regardless of its inputs .. i would add below my php code for validation and the html code of the form that i wish to validate it .. please keep in mind that i'm new to this , so you might see some newbie code and mistakes , thank you for taking time to check my question.

<?php
// define variables and set to empty values
$staffErr = $emailErr = $subjectErr = $problemErr = $descriptionErr= "";
$staffname = $email = $subject = $problem_type = $description = "";

// staff name validation:
if ($_SERVER["REQUEST_METHOD"] == "POST") {
  if (empty($_POST["staffname"])) {
    $staffErr = "Staff Name is required";
  } else {
    $staff_name = test_input($_POST["staffname"]);

    // check if name only contains letters and whitespace
    if (!preg_match("/^[a-zA-Z-' ]*$/",$staffname)) {
      $staffErr = "Only letters and white space allowed";
    }
  }

  // email validation:
  if (empty($_POST["email"])) {
    $emailErr = "Email is required";
  } else {
    $email = test_input($_POST["email"]);

    // check if e-mail address is well-formed
    if (!filter_var($email, FILTER_VALIDATE_EMAIL)) {
      $emailErr = "Please enter a valid email.";
    }
  }

  // subject validation:
  if (empty($_POST["subject"])) {
    $subjectErr = "Subject is required";
  } else {
    $subject = test_input($_POST["subject"]);

    // check if subject only contains letters and whitespace
    if (!preg_match("/^[a-zA-Z-' ]*$/",$subject)) {
      $nameErr = "Only letters and white space allowed";
    }
  }
    
  // problem type validation:
  if (empty($_POST["problem_type"])) {
    $problemErr = "Problem type is required";
  } else {
    $problem_type = test_input($_POST["problem_type"]);
  }

  // description validation:

  if (empty($_POST["description"])) {
    $descriptionErr = "A Description is required";
  } else {
    $description = test_input($_POST["description"]);
  }
}

function test_input($data) {
  $data = trim($data);
  $data = stripslashes($data);
  $data = htmlspecialchars($data);
  return $data;
}
?>


<form  method="post" onsubmit=" return formSubmit(), test_input() " action="insert_logs.php">
  <div class="error1" id= "errorMsg">* Required Fields</div>
    <div class="error" id= "errorMsg1">*<?php echo $staffErr; ?></div>
    <div>
      <label for="staff_name"><b>Staff Name:</b></label> 
      <input  class="field" id="staff_name" name="staffname" onclick=" return staffValidation()" onchange=" return staffValidation()" id="subject" type="text" placeholder="Staff Name" value="<?php echo $staffname;?>"  > 
    </div><br>
    <div class="error" id= "errorMsg2">*<?php echo $emailErr; ?></div>
     <div>
       <label for="email"><b>Email:</b></label> 
       <input class="field" id="email1" name="email" onclick=" return emailValidation()" onchange=" return emailValidation()" type="email" placeholder="staff@wearview.com" value="<?php echo $email;?>">  
      </div><br>
      <div class="error" id= "errorMsg3">*<?php echo $subjectErr; ?></div>
      <div>
        <label for="subject"><b>Subject:</b></label> 
        <input  class="field" name="subject" id="subject1" onclick=" return subjectValidation()" onchange=" return subjectValidation()" type="text" placeholder="Subject Title" value="<?php echo $subject;?>" > 
      </div><br>
      <div class="error" id= "errorMsg4">*<?php echo $problemErr; ?></div>
      <div>
        <select onclick=" return problemValidation()" onchange=" return problemValidation()" class="field4" name="problem_type" id="problemtypes">
          <option value="">Problem Type</option>
          <option value="Hardware">Hardware</option>
          <option value="Software">Software</option>
          <option value="Software&Hardware">Software & Hardware</option>
          <option value="Other">Other</option>
        </select>
      </div><br>
      <div class="error" id= "errorMsg5">*<?php echo $descriptionErr; ?></div>
       <div>
         <textarea class="field2" id="description1" name="description" onclick=" return descriptionValidation()" onchange=" return descriptionValidation()" placeholder="Description goes here" value="<?php echo $description;?>"  rows="15" cols="90"></textarea>
       </div>          
       <div>
         <button class="field3" type="submit" class="btn">Submit</button>
         <input type="checkbox" id="notify" name="notify" value="">
         <label for="notify">Inform me by email when issue is resolved.</label> 
       </div>
     </form>

The form, thank you for taking time to check them