Inverse of symmetric static arrays returns errors

MWE:

using LinearAlgebra
using StaticArrays

my_matrix = [
    23.839174539658693 243552.4933521217 1.8416855269559405e9 7262.007338486136 -0.15093214378094674 -0.08311979038696746; 
    243552.4933521217 2.962601669841655e9 1.565059094802e13 7.454589007612145e7 -1822.7229289215243 -703.6834309479851; 
    1.8416855269559405e9 1.565059094802e13 1.852842171814476e17 5.52741246224e11 -9.820212598493524e6 -8.437622282150278e6; 
    7262.007338486136 7.454589007612145e7 5.52741246224e11 2.214925230782032e6 -46.13837676487657 -24.926993518175713; 
    -0.15093214378094674 -1822.7229289215243 -9.820212598493524e6 -46.13837676487657 0.0011236787686097864 0.00044192488231854755; 
    -0.08311979038696746 -703.6834309479851 -8.437622282150278e6 -24.926993518175713 0.00044192488231854755 0.0003843024068388386
    ]
my_static_matrix = @SMatrix[
    23.839174539658693 243552.4933521217 1.8416855269559405e9 7262.007338486136 -0.15093214378094674 -0.08311979038696746; 
    243552.4933521217 2.962601669841655e9 1.565059094802e13 7.454589007612145e7 -1822.7229289215243 -703.6834309479851; 
    1.8416855269559405e9 1.565059094802e13 1.852842171814476e17 5.52741246224e11 -9.820212598493524e6 -8.437622282150278e6; 
    7262.007338486136 7.454589007612145e7 5.52741246224e11 2.214925230782032e6 -46.13837676487657 -24.926993518175713; 
    -0.15093214378094674 -1822.7229289215243 -9.820212598493524e6 -46.13837676487657 0.0011236787686097864 0.00044192488231854755; 
    -0.08311979038696746 -703.6834309479851 -8.437622282150278e6 -24.926993518175713 0.00044192488231854755 0.0003843024068388386
    ]

my_symmetric_matrix = Symmetric(my_matrix)
my_symmetric_static_matrix = Symmetric(my_static_matrix)

myinversion = inv(my_symmetric_matrix)
mystaticinversion = inv(my_symmetric_static_matrix)

Returns

ERROR: LoadError: MethodError: no method matching bunchkaufman!(::Symmetric{Float64, SMatrix{6, 6, Float64, 36}}, ::Bool; check=true)

On Julia 1.6.0

Apologies for the unnecessarily large matrix, I'm copying this from some work I was originally trying to do for a model I'm getting the covariance matric of through the inverse Hessian.

Start by reproducing the MWE on Julia 1.6.0 with StaticArrays and compare inv(Symmetric(my_matrix)) against inv(Symmetric(my_static_matrix)). Trace the failing bunchkaufman! call and confirm that inversion of the symmetric SMatrix completes without the reported MethodError.