Here's an MWE where there's a 100x performance drop due to hitting the generic dot fallback when taking the inner product of a sparse array with the adjoint of a sparse array:
julia> using SparseArrays, LinearAlgebra, BenchmarkTools
julia> let N = 1000
A = sprand(N, N, 0.1)
At = spzeros(N, N)
adjoint!(At, A)
@btime $At ⋅ $A
@btime $A' ⋅ $A
end;
509.345 μs (0 allocations: 0 bytes)
32.945 ms (0 allocations: 0 bytes)