As seems usual for Sigma telephotos, it has relatively poor image stabilization. It seems virtually identical to that of the el cheapo Sigma 150-600mm C, being 3 ev or less for most of its working range:
https://www.lenstip.com/510.3-Lens_review-Sigma_S_500_mm_f_4_DG_OS_HSM_Build_quality_and_image_stabilization.html
“The maximum distance between both curves reaches 3.5 EV and such is, in our opinion, the stabilization unit efficiency. It is a result a bit lower than the declared one but still good enough, allowing you to work with comfort at such long focal lengths.”
https://www.lenstip.com/434.3-Lens_review-Sigma_C_150-600_mm_f_5-6.3_DG_OS_HSM_Build_quality_and_image_stabilization.html
“It is clear that the maximum distance between both curves amounts to 3.0-3.3 EV and such is, in our opinion, the tested lens’s stabilization system efficiency. It is a good result but hardly a record-breaking one.”