Why is the apostrophe converted to &#039; in account activation e-mail?
The easiest way to fix this is simply set the formatter to the Default PHP Mailer, if you want to stick to plain text mail.

This is a known bug in the SwiftMailer module where Html::escape is called, even for plain text. Bug report here: https://www.drupal.org/project/swiftmailer/issues/2937293 .

The Html::escape function declares:

  /*
   * This method escapes HTML for sanitization purposes by replacing the
   * following special characters with their HTML entity equivalents:
   * - &amp; (ampersand) becomes &amp;amp;
   * - " (double quote) becomes &amp;quot;
   * - ' (single quote) becomes &amp;#039;
   * - &lt; (less than) becomes &amp;lt;
   * - &gt; (greater than) becomes &amp;gt;
   */


And that's where your &amp;#039; comes from.