I'm not going to be much help, but I can confirm that the "hamburger" doesn't appear to have any life, where as the "<" and ">" buttons in the regular part of the page do change the date displayed. This is with Chrome on a Samsung G8.
Opening the page in Firefox on my desktop has a conventional menu that drops down the two login options.
I don't know too much about website developer tools on Android itself, but perhaps you can use a simulator environment to watch more closely what the JS is doing.
Some sites have an "m." variant of the address to signal "mobile environment" and you can use that address on a desktop browser to play with the mobile interface, but I don't think web2py has that built-in. PythonAnywhere might have that as a feature, but that wouldn't help because web2py would still see the desktop user agent.
Oooh, I just tried narrowing the desktop window, and the menu bar switched to hamburger, and the hamburger is silent. Turning on FF inspector, I see two errors on the console:
The second error may be relevant.
Dave S
/dps