Nostr based OS? You can't make an OS out of a layer on top of http...
Nostr can provide connections for many apps though. I find it fits perfectly with my selection of tech that I own, like GrapheneOS
Discussion
You can integrate it in the base layer. nostr:nevent1qqs03zthxg9yzajpn94ngpatv3v252gu0t095ux65gpgtllcfpyg7zqpr3mhxue69uhkjmnwv4ezuum9vfshxarf0qh8xmmrd9skctczyrlmedcxnaa2t4kmz20t88na32tcj3ndy4dxx7avr6lcv9as2aqygqcyqqqqqqg44phjp
I like the current GrapheneOS to be very light. Apps on top of it can use nostr as much as possible, so I don't see the advantage of putting it at the base level.
It doesnt have to be GrapheneOS, I mean more in generic. Some OS'es / forks can do this. I loved stock Android and ChromeOS because I had everything available after signin with my Google account. But it should not be centralized big tech, as we know the disadvantages.