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Also @Muppetteer
Hand saw, plane, and 1/2" router with a decent size chamfer bit and various sized straight fluted bits could get the job done.....
As you say, you could do it with purely hand tools but the skill and experience levels needed are high.
I would put money on there being dominos re-enforcing the mitres at the corners though. Either that or the drawer boxes are designed to fail as mitres, even with hi spec resin-based glue, aren't strong enough joints to withstand pulling like that long term. The cheaper/easier way to re-enforce them would be with splines.
You’re going to struggle to achieve that with hand tools.
I would say you’d need access to a track saw or table saw.
Not really sure how they’ve joined the bottom - assume a dado then some fixing nails for the strengthening piece.