Different numerical results on 1.10 and 1.9.4

Hi,

I just found out that 1.9.4 and 1.10 give different results for a matrix multiply:

using StaticArrays
rotmatrix2d(a) = @SMatrix [cos(a) sin(a); -sin(a) cos(a)]
rotate(a, p) = rotmatrix2d(a) * p 
rotate((pi / 4), SVector{2}(0.42095778959006, -0.42095778959006))
# Julia 1.10
[2.8053096100683734e-17, -0.5953242152248626]
# Julia 1.9.4
[7.419375817039376e-17, -0.5953242152248626]
# Julia 1.6.7
[2.8053096100683734e-17, -0.5953242152248626]

julia> versioninfo()
Julia Version 1.10.0-rc1
Commit 5aaa948543 (2023-11-03 07:44 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 16 × AMD Ryzen 7 5800H with Radeon Graphics
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
  Threads: 11 on 16 virtual cores
Environment:
  JULIA_PKG_OFFLINE = true
  JULIA_PKG_PRECOMPILE_AUTO = 0
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 8

# same machine
julia> versioninfo()
Julia Version 1.9.4

Start by reproducing the supplied StaticArrays matrix-multiplication example on Julia 1.10, 1.9.4, and 1.6.7 on the reported Windows setup. Trace the differing result through the relevant StaticArrays and Julia numerical behavior; done means determining whether the discrepancy is a bug and documenting or covering the confirmed behavior with a regression test.