Hi,

You can try to use t-esc instead of the t-out 

<p>
  Regards,
  <br/>
<span t-esc="user.name"/>
  <br/>
<span t-esc="user.employee_id.job_title"/>
  <br/>
Phone: <span t-esc="user.partner_id.phone"/>
  <br/>
Email: <a t-attf="mailto:#{user.email}"><span t-esc="user.email"/></a>
</p>

user.name: This will dynamically insert the user's name.

user.employee_id.job_title: This will retrieve the user's job title from their linked employee data.

user.partner_id.phone: This will insert the user's phone number from their partner data (assuming phone number is stored in the partner record).

user.email: This will display the user's email address.

mailto:#{user.email}: This will create a mailto link for the email address.
Make sure you're using these expressions within the appropriate t tags to make them properly evaluated in Odoo's templating system. If you're still encountering issues with the HTML code getting cleared out when you save, it could be due to certain restrictions or validation in the email signature field. If that's the case, you might want to consult Odoo's documentation or support resources for specific guidance on how to achieve dynamic email signatures.

Remember to back up your code before making any significant changes, and test your code in a controlled environment before applying it to your live Odoo instance.

Hope it helps