`gradient!` allocates for matrices but not for vectors

Is it due to views?

julia> using ForwardDiff, Chairmarks

julia> g(x) = sum(abs2, x)
g (generic function with 1 method)

julia> @be (zeros(2), zeros(2), ForwardDiff.GradientConfig(g, zeros(2))) ForwardDiff.gradient!(_[1], g, _[2], _[3])
Benchmark: 3548 samples with 1255 evaluations
min    18.855 ns
median 19.215 ns
mean   19.753 ns
max    62.914 ns

julia> @be (zeros(2, 2), zeros(2, 2), ForwardDiff.GradientConfig(g, zeros(2, 2))) ForwardDiff.gradient!(_[1], g, _[2], _[3])
Benchmark: 2765 samples with 365 evaluations
min    67.745 ns (4 allocs: 160 bytes)
median 77.912 ns (4 allocs: 160 bytes)
mean   87.240 ns (4 allocs: 160 bytes)
max    220.408 ns (4 allocs: 160 bytes)

Reproduce the vector and matrix benchmarks in the issue using ForwardDiff and Chairmarks. Start by tracing the gradient! call and comparing its behavior for vector and matrix inputs, especially whether views are involved. Done means identifying and addressing the matrix-only allocations, with the benchmark showing the resulting allocation behavior.