Some of the bridges are, for example, a series of : commands (which are translated into comments not to screw the shell). Also, if you highlight text and do Ctrl Shift T you paste the text directly into the terminal.
So the integrated terminal is an actual terminal (and there are actually some bridges between the terminal and the browser).
As you can see it can handle complex TUIs without issues.
It needs more improvements and fix details, but, I am posting this from here after all.