Palpatine was totally incapable of love or compassion. He was only concerned about restoring Anakin as best as possible and then using whatever power Anakin had solely for the Emperor's benefit. Palpatine believed that with Vader in this more weakened condition, he would also be more easily controlled.
Even though Palpatine's kindness towards Anakin was always fake, he still had respect for Anakin's power. But now that Anakin is beaten and scarred, Palpatine has lost all respect for him. Up to Star Wars: Episode VI - Return of the Jedi, Palpatine treats Vader poorly, and they very much have an abusive relationship.
He has shown no affection for anyone throughout the films and tv shows. Sure he will say “my friend” to Vader but in the end, Palpatine only viewed him as a piece in his quest for absolute domination/power. The same can be said for Vader too.
Short Answer: He was mad and sad. Long Answer: It's been shown many times in the Star Wars prequel era that Palpatine “cared” about Anakin as a son and even referred to him such as a term of endearment towards him.
Strictly speaking, Palpatine didn't NEED Anakin to carry out his plan to become Emperor, or to turn the Republic into the Empire. He more or less took care of that on his own. But he could tell that Anakin had the potential to become the most powerful Jedi of all. In Episode II, he said this directly.
Star Wars: The Rise of Skywalker hints at Palpatine's real purpose for Darth Vader. It's an open secret that Palpatine was disappointed with Darth Vader; he thought he was getting the Chosen One, a force of nature who could not be beaten, and yet Darth Vader was defeated the moment he crossed blades with an adult Jedi.
Given the physical and psychological trauma he had gone through since Star Wars: Episode III - Revenge of the Sith, Darth Vader wasn't confident enough that he can succeed if he antagonized Emperor Palpatine.
Palpatine admits to Darth Vader that the Jedi he actually feared most was none other than Jocasta Nu.
If Qui-Gon had survived his fight against Darth Maul, he would have sensed Palpatine's evil, and Anakin wouldn't have become Darth Vader. Thus, while Qui-Gon was less powerful than Yoda, Palpatine feared him more.
Yes, his entire character since then was a self loathing tragic monster who has little reason to care about anything. Betraying Mace Windu instantly made him regret his act of impulse, Padme's death and rejection of his actions later on made it stick.
Palpatine's patience and flexibility paid off as he coaxed the galaxy into war and then rescued it. The Emperor who formed the Imperial Senate was viewed as a savior of sorts. He stopped the all-powerful Jedi and brought peace to planets ravaged by the Clone Wars.
In Disney Canon: Galius Rax. Rax was a boy that Palpatine met from Jakku. Rax became a trusted adviser to Palaptine, and Palpatine entrusted Rax with his contingency plan.
If Maul knew, he would have tole Obi Wan or another Jedi during the Clone Wars. Dooku knew Palpatine was Sidious as he told Obi-Wan about him controlling the senate and referred to him as the dark lord. There's no real way of actually knowing if he knew ab palpatine.
Palpatine began abusing Anakin right from the word “go”, and from the moment he clapped eyes on the kid in The Phantom Menace. What he did at first was known as “grooming”. Now, some people don't fully understand what grooming entails, and the process of how Palpatine groomed Anakin.
He regretted it the moment he did it. He asked himself what he just did, dropped his lightsaber, and was visibly ashamed of himself when Palpatine anointed him a Sith Lord and began his speech about wiping out the Jedi.
Emperor Palpatine should have known Darth Vader would betray him in Return of the Jedi, but he was blinded by his arrogance and ignorance. Palpatine couldn't predict Darth Vader's betrayal in Return of the Jedi for one simple, yet very powerful reason.
In non-canon material it is said that Palpatine had a number of concubines and never took a wife in fear that he would produce a legitimate heir. One of these non-canon concubines was Roganda Ismaren, a former Jedi who survived Order 66, and lived for a time at Palpatine's side.
Aware that the Jedi Order could be destroyed, Windu sought to prevent this outcome by leading a team of fellow Jedi Masters, Kit Fisto, Saesee Tiin, and Agen Kolar, who were among the finest warriors in the Order, to arrest Palpatine, leaving Skywalker behind.
As powerful as Darth Sidious may have been, it's easy to forget he actually seemed afraid of Master Yoda.
Even after his brutal scorching in the fires of Mustafar, sand remained the only natural phenomenon that Vader feared. To him, sand was a reminder that he'd failed to save his mother or Padme from death.
Much like Palpatine, Darth Caedus was able to take control of the galaxy but he didn't lead nearly as long. However, his reign was still full of brutality and in a lot of ways, he was worse than Palpatine.
The reason Vader never successfully overthrew the Emperor wasn't from lack of ambition, but more from a lack of allies. Even in Revenge Of The Sith Anakin planned to surpass Palpatine by telling Padme that they could overthrow the Chancellor and rule the galaxy together.
Yes Vader knew Sidious manipulated him. In the Darth Vader (2017) comics he declares that he knows Emperor Palpatine had been lying to him about the Dark Side's ability to cheat death. In fact right from the very start, when he came off the operating table and was told Padme was dead, he realised Sidious had used him.
It was for that love that Vader killed Palpatine, but according to Darth Sidious himself, it was a "pathetic display" and "all for nothing," because in the end, Darth Vader sacrificed his own life yet "the Sith would return."