We did this sort of thing at SFU some 25-30 years ago; though we stopped short of running an OS and compiler on it, and it wasn't a group project.
For those interesting in trying this sort of experiment, but wish to have some guidance and accessible tooling, I highly recommend Turing Complete; you'll go from a few gates to a full computer. Components can be shared with the community; where you'll find things like a RiscV core and such. Anyhow, it's great fun. Do recommend. It's on Steam:
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