`mul!` does not respect false as a strong zero

[tam724]

For e.g. Float16 where mul! (mat-vec) does not call BLAS, but the generic julia implementation, the resulting vector after mul! with α, β = false, false still contains NaNs.
Here's a MWE:

julia> using LinearAlgebra

julia> x, A, y = fill(NaN32, 2), fill(NaN32, 2, 2), fill(NaN32, 2)
(Float32[NaN, NaN], Float32[NaN NaN; NaN NaN], Float32[NaN, NaN])

julia> mul!(y, A, x, false, false) # stops the NaN propagation
2-element Vector{Float32}:
 0.0
 0.0

julia> x, A, y = fill(NaN16, 2), fill(NaN16, 2, 2), fill(NaN16, 2)
(Float16[NaN, NaN], Float16[NaN NaN; NaN NaN], Float16[NaN, NaN])

julia> mul!(y, A, x, false, false) # does NOT stop the NaN's
2-element Vector{Float16}:
 NaN
 NaN

julia> X, A, Y = fill(NaN16, 2, 2), fill(NaN16, 2, 2), fill(NaN16, 2, 2)
(Float16[NaN NaN; NaN NaN], Float16[NaN NaN; NaN NaN], Float16[NaN NaN; NaN NaN])

julia> mul!(Y, A, X, false, false) # however, matmatmul does
2×2 Matrix{Float16}:
 0.0  0.0
 0.0  0.0

I tried with julia 1.11.5 and 1.12.0-beta4.