When I receive an email sent by someone using a webmail service (e.g. Gmail, etc.), I can find the IP address of the sender's email server in the email headers.
But do the email headers also contain the IP address of the desktop (client) computer used by the person who sent the email?
Would it be the case if they use something like Thunderbird instead of webmail?
I have read Email headers from messages sent via Gmail online client contain private IP addresses. What are these addresses? and its answers, but I am not 100% sure if there are cases for which the client computer's IP address (where Gmail in the browser, or Thunderbird desktop client, is open) are disclosed.
More precisely, this comment "A desktop mail application is itself the SMTP client" + "The Received: header contains the address of the SMTP client" seems to imply that the IP address of the computer where Thunderbird is running could be in the headers. Is that true?