My email send with Thunderbird (latest build) leaks my IP within the Email Header.

Any time you connect to the outside world via SMTP to send an email, the IP will be logged in the headers. It's part of the protocol. Why is this a concern? When using the Internet you aren't anonymous. It's just the way it is, unless you use a service like TOR.

I've tested this with www.emailipleak.com

What does emailipleak.com do or test? In any case, you just need to check the headers of the received message to see the IP of the sending host.

I believe it is unnecessary, that the receiver can track my IP (the IP assigned from my ISP) so easily from the Email Header. Another strange thing is: One specific email account doesn't leak my IP, but other accounts from other email providers do. There must be an option that I'm not aware of.

This is my result for the test if the Email leaks the IP emailipleaktest.com:

I believe it is unnecessary, that the receiver can track my IP (the IP assigned from my ISP)

As said before, it's part of the protocol. What I don't understand is what you're concerned about. Whatever you do when connecting to the Internet (not only when sending mail, but also when accessing a web site), your computer is identified by your IP address, and you leave traces all over the place.

One specific email account doesn't leak my IP

I'd suggest you talk to your email provider and ask them what they do to hide your sending host IP.

This is my result for the test if the Email leaks the IP

It is a miracle to me why you'd want to run this test. You're concerned about disclosing your IP, but you happily give it to a web site you probably know very little about.