How can I set a minimum number of characters when entering an ad password?

No, but can be easily changed by adding minlength property to input

I added to form_passwrd.php, minlength="6" and required so that users are required to enter a password of at least 6 characters.
Here is the whole file:
<?php 
  $item_my = ModelBO::newInstance()->getItem($item_id); 
?>

<link href="<?php echo osc_base_url(); ?>oc-content/plugins/backoffice_manager/css/form.css" rel="stylesheet" type="text/css" />

<div class="row">
  <div id="bo_mgr_table">
    <label for="bo_mgr_passwrd"><?php _e('Enter Password', 'backoffice_manager'); ?></label>
    <input type="text" style="float:left;" name="bo_mgr_passwrd" id="bo_mgr_passwrd" value="<?php if($item_my['passwrd'] <> ''){echo $item_my['passwrd']; } else { echo Params::getParam('passwrd'); } ?>" size="20" minlength="6" maxlength="20" required />
    <div class="bo_info"><?php _e('Used to edit this listing', 'backoffice_manager');?></div>
  </div>
</div>

The following problem occurs: When I have the booking plugin activated, the message for correct password completion appears at the top, while when I disable booking, the message appears below the password box, which is probably the correct one.

You mean error message? I think it should be on top.

However, when the booking plugin is enabled, the message appears below the password box, as shown in the photo. How can I make it appear below the password box with the booking plugin disabled? This way it is easier for users to see.

And why does the booking plugin affect the display position of the message?

That's interesting, but it's backoffice, not important. You probably has some jquery conflict?

How is this detected and how is it corrected?

In backoffice, check browser console.

Because as I told you, by displaying the message below the password box, it is easier for users to see it, how can I do that?

Booking plugin was updated.
It relates to jquery validate script, there are options to show just one error box or to show it below inputs. You will need to check it's documentation and reference.

Do you mean the documentation and the reference for the Backoffice Manager Plugin? I have deleted the booking plugin because I don't need it.

Documentation of jquery validate:
https://jqueryvalidation.org/

Thanks for the suggestion, but this is difficult for me to do on my own.

The way this demo https://jqueryvalidation.org/files/demo/ works is very useful for users and I believe that in the future it should be introduced into user logins and every form that requires data.