This is not correct and I'm curious what you're basing it on. The most powerful bomb we ever detonated (Tsar Bomba at 50 Mt) got something on the order of 96-97

This is not correct and I'm curious what you're basing it on. The most powerful bomb we ever detonated (Tsar Bomba at 50 Mt) got something on the order of 96-97% of its energy from fusion with its 2-stage test design (tamper replaced with lead). It's true the full power 100 Mt 3-stage with a U-238 tamper would have gotten vastly more from fission (at the cost of terrifying levels of fallout), but it didn't need it. Castle Bravo, the biggest US bomb ever tested, was also heavily fusion (and big thanks to the unexpected lithium 7 tritium bonus), though I think you're right that a lot of ultimate yield was from fission of the natural uranium tamper. It did directly lead to the Mk-21 though, tested in Redwing Navajo at 4.5 Mt and 95% fusion I think? It's true that placing a fusion bomb in a uranium case can massively boost the yield of any single explosive, and in a full fission-fusion-fission design a good half the energy can come from fission. It's not required to work though, a transparent casing can be chosen too, that's the whole concept behind neutron bombs and "low-yield" weapons after all. I'm no expert for sure, this is just my understanding from reading some of the archives and such, so I'd be curious to read any other sources you have.