8 bit is not absent in x86 SIMD, it is a slightly less covered than 32 & 16 bit, but you can fully implement all the common 8 bit ops and most are 1 instruction(with AVX2). There are even various horizontal ops on 8 bit values(avg, dot etc).
Also AVX512 is way more common than SVE2, all Zen4 & Zen5 support it.
More specifically, basically the only absent 8-bit ops that have 32-bit equivalents in AVX2 are shifts and multiplies. Shifts are quite annoying (though, with a uniform shift they can be emulated on AVX-512 via GFNI abuse in 1 instr), multiplies are rather rare (though note that there is vpmaddubsw for an 8-bit→16-bit multiply-add). There's even a case of the opposite - saturating add/sub exist for 8-bit and 16-bit ints, but not wider.
GFNI is distinct from AVX-512; it was merely introduced in cores that also had AVX-512.