As far as I recall, you can download code to your desktop but not your laptop, unless you’re doing something like iOS development that would be difficult to do over say ssh -Y.
I'm not a googler, but from my readings about their dev culture: it wouldn't be practical, as such, for a lot of what that dev server is really used for. Stupid-much development, however, is API driven and based on isolated logic. Those individual components or spike solutions would make absolute sense on the laptop.
More importantly: with the kinds of operations Google is running these days you'd really expect lots of the APIs youd need for product development to be readily accessible.
So, yeah, you'd be hacking on your laptop separately, and maybe doing some kinds of work. They run a monorepo, though, so it'd be of a somewhat peripheral nature. Proper dev is what the dev station is for.
You can't run minikube on a dumb terminal while off at a conference.