It depends on what kind of signature is offered by the mail app on your phone. Most of them at least allow a string of plain text, but some may allow HTML or an image. If you send from the webmail page instead of through a mail app, you might be able to create an HTML signature, e.g. from gmail.com or outlook.com you can use HTML.

I use the thunderbird app. Not possible there?

Thunderbird does not run on phones or tablets so you are not using Thunderbird on your phone.

There may be mobile apps with 'thunderbird' in the title, but there is no mobile version of the TB used on desktop operating systems.

Apparently I had BlueMail.

Cheers

https://bluemail.help/custom-signatures/

"HTML Support is coming soon!"