Aren't most bomb designs these days "mostly fission" - with most of the energy in most H-bomb designs coming from fission of the secondary tamper by the neutrons from the fusion stage?
Yes, that's always been the case as I understand. The fusion stage is to get the bomb to do its exploding thing before it propels itself apart and thus just scatters debris everywhere.
"(3) The fusion fuel of the secondary stage may be surrounded by depleted uranium or natural uranium, whose U-238 is not fissile and cannot sustain a chain reaction, but which is fissionable when bombarded by the high-energy neutrons released by fusion in the secondary stage. This process provides considerable energy yield (as much as half of the total yield in large devices), but is not considered a tertiary "stage". Tertiary stages are further fusion stages (see below), which have been only rarely used, and then only in the most powerful bombs ever made."
Most H-bomb designs have a (fusion) boosted fission primary, then a fusion secondary that has itself a boosted fission "spark-plug", then fusion then fission of the secondary tamper by the neutrons from the secondary fusion stage - with this latter fission stage contributing most of the energy.