Browser side checks don’t reveal the complete picture. And in some cases, paint the wrong picture.
Android’s killswitch is under the control of the end-user. These are named “Always-on VPN” and “Block connections without VPN” (in English), and both must be turned ON for your VPN app, from Android’s VPN settings.
Note that, on Android (and on most OSes), some high privileged apps (mostly OEM and Google apps), which are typically pre- installed (some you can disable but none can you uninstall), do retain the capability to bypass the “killswitch”. A network monitor project I co-develop keeps track of such bypasses in AOSP here: Show Android components that can bypass VPN even in lockdown mode · Issue #224 · celzero/rethink-app · GitHub
And even if (hypothetically) AOSP never allowed such a bypass, the OEMs can change that behaviour for their Android distribution (unfortunately, as of Android 16, as part of its compatibility requirements, Google doesn’t enforce OEMs confirm to “Block connections without VPN” (ref / mirror).
Not quite sure, as it depends on the commands being run by wg-quick on up and down on your setup. Which setup guide are you using?
They’ve recently added “light weight” anti-censorship measures, too. That said, I consider custom features such as DAITA a form of lock-in. I’d not worry about it too much, if I were you.