The Android Gmail app currently doesn’t support any signatures in HTML.

You are not alone in being disappointed that this is still not a thing despite years of urgencies from developers and users.

We are monitoring the situation and whenever Google decides to add support for rich text, HTML styled signatures, we will implement it ASAP.

A functional (but not so comfortable) workaround is to user the web version of Gmail on your phone.

Go to your phone's web browser, navigate to mail.google.com, log in with your account, ignore the prompts to switch to the app, and compose your emails right there.