gra123d Can an evil smart monitor read the contents of Downloads folder then?
It is very unlikely but theoretically possible. I would trust monitors more that are made by large companies with important reputations.
gra123d I imagine GrapheneOS team would have considered desktop mode a vulnerable feature if that were the case... or maybe it is an understood trade-off?
At present it's in Developer Options, which have zero expectation of safety.
When Google actually ships it for users, presumably they will have spent some time on it being reasonably secure. The GrapheneOS team may look through the code... but keep in mind that many users will want to use it right away, unless it were widely known to have serious holes -- and some people would use it anyway!
Given the complexity of the USB protocol stack, and the things that run on top of it, plugging anything into the USB port poses some risk. Also, turning Wi-Fi on, or turning the cellular modem on, or downloading an app, all pose some risk.
gra123d (Perhaps GrapheneOS mod will have a definitive answer to this)
There isn't one. Since the code hasn't shipped yet, it hasn't been exploited yet, so it can't be definitively unsafe. Given present security technology, nothing that complex can be definitively safe.
Plugging a Pixel into a "dumb" monitor should be pretty safe. Plugging a Pixel into an Internet-connected "smart TV" made by a company with a reputation for spying on users is probably less safe.