Why Did Palpatine Love Maul's Lightsaber?

Because of what it told his master. Sidious trained Maul as an assassin rather than a Sith Lord, and the brutal, ancient double-bladed lightsaber advertised exactly that. It made Maul read as a weapon rather than a successor, which kept Darth Plagueis comfortable and stopped him noticing that his own apprentice was already planning his death. (The Phantom Menace; Darth Plagueis)

An apprentice built wrong on purpose#

Maul's training was unconventional from the start. It focused almost exclusively on advanced lightsaber combat, and the results are on the record: an acrobatic, relentlessly drilled fighter who could twirl a saberstaff one-handed and pursue an enemy without ever letting up. (The Phantom Menace; Darth Plagueis)

That should look odd, because Palpatine did not rate lightsabers especially highly. His whole view of power placed the blade well behind mastery of the Force. Building an apprentice around the one thing he considered secondary is not an oversight from a man who did nothing by accident. (Dark Lord: The Rise of Darth Vader)

It was the point. The emphasis was deliberate, and it was about what Maul was for. (Darth Plagueis)

Assassin, not Lord#

Maul was being built as a Sith assassin. Not a Sith Lord, not an heir, not the next link in the chain. (Darth Plagueis)

Understanding why means understanding what the Rule of Two actually demands. Darth Bane's decree holds that only two Sith exist at any time: a master to represent the power of the dark side, and an apprentice to crave it and train under the master until they are ready to fill that role. The mechanism is brutal by design. The apprentice is supposed to kill the master and take their place, which is what forces each generation to be stronger and more cunning than the last. It also means the relationship never contains any trust, because both parties spend it watching each other for weakness. (The Phantom Menace; Darth Bane: Path of Destruction)

Plagueis set the terms himself. A year after Sidious took the infant Maul, Plagueis gave him permission to train the boy, but told him not to share their most treasured secrets: Maul was to be an assassin, not a Sith Lord like the two of them. A real apprentice, someone genuinely trained to become a Sith Lord, would have been a rival in waiting. (Darth Plagueis)

So Sidious kept to the letter of it. He had an apprentice who could never satisfy the spirit of the rule. Maul filled the slot, and he was trained as a tool rather than a candidate. (Darth Plagueis)

Why a saberstaff specifically#

The weapon fitted that story, and it worked on two audiences at once.

The first was the Jedi, who had little experience of a double-bladed lightsaber, and there is good reason for that. The design goes back to the mythical Sith Lord Exar Kun in the Qel-Droma Epics, which puts it firmly in the category of things Jedi had read about rather than fought, and in Legends saberstaffs stayed obscure weapons for centuries. Against a Padawan and his master on Naboo, Maul came close to winning outright. (Gadgets and Gear; Darth Bane: Path of Destruction; The Phantom Menace)

The second audience mattered more. A saberstaff is brutal and it is ancient, and both qualities say the same thing about whoever carries one. This is a warrior, not a master. A weapon of pure destruction wielded by an instrument of pure destruction. (The Phantom Menace; Gadgets and Gear)

That reading is exactly what Sidious wanted circulating. Every time Plagueis looked at Maul, the weapon in his hands reinforced the conclusion that he posed no threat to the grand Sith plan. (Darth Plagueis)

The furnace#

There is a detail from Legends that makes the whole arrangement sharper.

Maul made his own crystals in a compression furnace. Not one crystal, four, because that is what a double-bladed lightsaber needs, and he spent four days in deep meditation, using the Force to control and monitor how they formed. Maul took considerable pride in it. (Darth Maul: Shadow Hunter)

Set that beside how Sidious himself thought about lightsabers. He was fairly disdainful of them, and once told Darth Vader the Sith used them mainly to humiliate the Jedi. (Dark Lord: The Rise of Darth Vader)

That tells you what the exercise was actually for. It was not about giving Maul the best possible weapon. It was about producing something that looked ancient, personal and dangerous, and about keeping a young Zabrak occupied and convinced of his own significance while his master got on with the real work. (Darth Maul: Shadow Hunter; Darth Plagueis)

What Plagueis saw#

Plagueis was obsessed with immortality, and so focused on it that he missed the signs that his faithful apprentice was progressing in a way that should have worried him. (Darth Plagueis)

Maul was one of those signs, disguised as a reassurance. In the novel Plagueis lives through Maul's training and dies the night Palpatine becomes Supreme Chancellor. Sidious presented his master with an apprentice who was visibly a blunt instrument, and Plagueis took that at face value. (Darth Plagueis)

He should have looked harder. The apprentice was never the point. The weapon was a message, and Plagueis read it exactly as intended, right up until Sidious killed him. (Darth Plagueis)