I think Legends Sidious was thought to be pure evil, always seeing everyone as a tool to use and dispose of when he was done with them. But what about Canon Sidious? I think I remember some source stating he really cared for Anakin when he found him half dead on mustafar. What about his niece Rey? Or his daughter? Or Gallius Rax?
By most accounts, Palpatine was basically a high-functioning sociopath. He was an expert at feigning actual relationships/emotions in order to get him what he wanted, but that's about the extent of it... In the end, all he truly cared for was power. Nothing more.
That being said, Ian McDiarmid had some interesting thoughts about Palpatine's 'feelings' back in Insider #82: https://i.imgur.com/mKEPkTb.jpg
The Aftermath novel claimed that Yupe Tashu was the closest thing the Emperor had to a friend. Though I imagine even that relationship was mostly void of any sense of companionship.
Palpatine rejected, as all sith do, happiness and fulfillment in favor of power. So he actively and consciously purged all compassion in his heart such that he could never care for anyone.
Though it is worth noting that the Revenge of the Sith novelization said that Anakin was his "shatterpoint."
Besides when he apparently had sympathy for the burnt Anakin, I can vaguely recall him feeling sick when Plagueis commanded him to kill Maul in the Maul: Lockdown novel, suggesting that he may have had some attachment to Maul, which is consistent with Plagueis's musing that Maul and Palpatine had an almost filial relationship in the Darth Plagueis novel.