Static analyzers find large numbers of hypothetical bugs, of which only a small subset are actionable, and the work to resolve which are actionable and which are e.g. "a memcpy into an 8 byte buffer whose input was previously clamped to 8 bytes or less" is so high that analyzers have little impact at scale. I don't know off the top of my head many vulnerability researchers who take pure static analysis tools seriously.

Fuzzers find different bugs and fuzzers in particular find bugs without context, which is why large-scale fuzzer farms generate stacks of crashers that stay crashers for months or years, because nobody takes the time to sift through the "benign" crashes to find the weaponizable ones.

LLM agents function differently than either method. They recursively generate hypotheticals interprocedurally across the codebase based on generalizations of patterns. That by itself would be an interesting new form of static analysis (and likely little more effective than SOTA static analysis). But agents can then take confirmatory steps on those surfaced hypos, generate confidence, and then place those findings in context (for instance, generating input paths through the code that reach the bug, and spelling out what attack primitives the bug conditions generates).

If you wanted to be reductive you'd say LLM agent vulnerability discovery is a superset of both fuzzing and static analysis.

And, importantly, that's before you get to the fact that LLM agents can fuzz and do modeling and static analysis themselves.