Short answer: no.
The long answer is that it’s a bit complicated. Screen res and DPI can’t be blocked unless you have a window manager that fakes the resolution (which AFAIK gos doesn’t). But gos does hide some stuff, I think they might be hiding CPU and baseband info (correct me if I’m wrong).
But the root / jailbreak part is something that’s verified through Google Play Integrity Checks. There’s been a fiasco a while back when Authy stopped working on gos, because of that play check. The same APIs are used by other programs from the Play Store to verify if the device is rooted. Of course, gos is not rooted (by design), but the integrity check is too dumb to realize that (it’s just checking some vendor signatures, i.e. google’s, to see if the kernel, initramfs and maybe other things are signed by that certificate and if not, the program refuses to work - the one’s that are the most egregious are usually banking programs, eeww, which people shouldn’t be using anyway fr fr, just use the website).
I know there were some discussions online about some linux privacy nutbar sending 2 known tracker / fingerprint testing sites to a graphene user and the user being bamboozled by how accurate the fingerprinting on vanadium was (showing the screen size, DPI, fingerprint accuracy etc. - because the browser doesn’t block javascript). I wish I saved that discussion, I can’t find it. So no, gos won’t protect you from being identified.
Though gos will prevent some programs from getting actual information about you with their sandboxing techniques (even google play), by giving it false location information, instead of accurate one (if you don’t allow location permissions to it - same for networking, it will pretend like it has given network permissions to a program, but it will act like the device isn’t currently connected to wifi, instead of telling programs that its request for network access was rejected, like android does it).
Setting a phone to airplane mode, to use as a wi-fi only device will completely disable the modem, but I think without physically removing it from the phone (which you can’t, it’s built into the SoC along wifi and BT), there will still be device identifiers related to it (unlike on pinephone, where you shut power off to the modem, completely cutting off any remnant of a device ID).
If you want privacy and getting close to anonymity, then qubes-whonix is the way to go. Make sure to disable JS if you don’t want tracking. If you are forced to use JS, you might want to use a browser that shares its fingerprint with everyone else using it (something like the TOR browser bundle, librewolf, or a hardened firefox profile that was customized to pretend the resolution is a certain common size). Obviously if you log into your device with accounts that lead to your identity, all these steps are for naught.
Back to your question, idk what links were used to show the fingerprintability of vanadium for that gos user, but I think they were fingerprint.com, fingerprintjs.com and / or thumbmarkjs.com.
