For anyone experiencing similar problems, another solution could be to build midori from source.
With midori v7.0.2 (latest you can install for raspberry os at the time of writing) I couldn’t get rid of the tab bar and some window borders. Building midori v9.0 from source it works nicely in full screen mode with the parameter -e Fullscreen. See description how to do that here https://github.com/midori-browser/core . There are also some related and resolved issues on github.