Reland " Avoid materializing arrays in bidiag matmul #55450" (#55777)

This relands #55450 and adds tests for the failing case noted in
https://github.com/JuliaLang/julia/issues/55727. The `addmul` tests that
were failing earlier pass with this change.

The issue in the earlier PR was that we were not exiting quickly for
`iszero(alpha)` in `_bibimul!` for small matrices, and were computing
the result as `C .= A * B * alpha + C * beta`. The problem with this is
that if `A * B` contains `NaN`s, this propagates to `C` even if `alpha
=== 0.0`. This is fixed now, and the result is only computed if
`!iszero(alpha)`.

Author: jishnub

stdlib/LinearAlgebra/src/LinearAlgebra.jl

@@ -673,7 +673,9 @@ matprod_dest(A::Diagonal, B::Diagonal, TS) = _matprod_dest_diag(B, TS)
 _matprod_dest_diag(A, TS) = similar(A, TS)
 function _matprod_dest_diag(A::SymTridiagonal, TS)
     n = size(A, 1)
-    Tridiagonal(similar(A, TS, n-1), similar(A, TS, n), similar(A, TS, n-1))
+    ev = similar(A, TS, max(0, n-1))
+    dv = similar(A, TS, n)
+    Tridiagonal(ev, dv, similar(ev))
 end
 
 # Special handling for adj/trans vec